Anonymous at Tue, 20 Aug 2024 15:31:53 UTC No. 16334628

Assuming you could somehow keep them alive and prevent the body from outright rejecting it, what would happen to someone who ingested several million calories from such as gasoline or radioactive elements

Anonymous at Tue, 20 Aug 2024 15:44:00 UTC No. 16334656

Why is here in the second term the sigmas contracted? I get they use the chain rule but shouldn't it be x mu instead of x sigma?

Anonymous at Tue, 20 Aug 2024 15:45:22 UTC No. 16334659

>>16334656
The covariant derivative is as follows

Anonymous at Tue, 20 Aug 2024 18:13:46 UTC No. 16334921

Is there anything to macro-pk? I know untrained people can't do micro-pk (proven via RNG experiments), but perhaps trained /x/tards can move spoons and shit

Anonymous at Tue, 20 Aug 2024 19:35:23 UTC No. 16335046

>>16334921
Of course there's nothing to it. It's complete /x/ bullshit.

Anonymous at Wed, 21 Aug 2024 11:49:15 UTC No. 16335977

>>16334617
Why is it valid to reorder the variables like this? Surely that changes the function as the domain must change?

Anonymous at Wed, 21 Aug 2024 11:59:32 UTC No. 16335982

Is /sci/ intelligent enough to explain this?

Anonymous at Wed, 21 Aug 2024 14:11:51 UTC No. 16336114

Let [math]G[/math] be a locally compact group and [math]\Gamma[/math] a countable, discrete cocompact subgroup. Suppose there is a pre-compact, open nbhd of the identity [math]U[/math] in [math]G[/math] that generates [math]G[/math] as a group. Is [math]\Gamma[/math] finitely generated?

Attempt at a proof: May assume [math]U[/math] is symmetric. Let [math]q: G \to G/\Gamma[/math] be the projection map. [math]q[/math] is an open map, so [math]\{q(U^n) : n = 1,2,3... \}[/math] forms an open cover of [math]G/\Gamma[/math], whence [math]\exists n[/math] such that [math]G/\Gamma = q(U^n)[/math]. I'd like to argue that [math]\Gamma \cap U^n[/math], which is a finite subset of [math]\Gamma[/math], is in fact a generating set for [math]\Gamma[/math], but the details evade me (assuming I'm right to begin with).

Anonymous at Wed, 21 Aug 2024 14:59:18 UTC No. 16336135

Ok so basically I'm looking for a book or resource that teaches science and knowledge about the world in concrete terms with examples and demonstrations rather than presenting some math or saying this is Fuck-Balls’ law. I want to see what experiments people use to get to the conclusions they have and how they have been used historically and in modern day. This applies to all knowledge of the world so in the beginnings it will talk about fire and how you use it to make things that burn better lile charcoal and then you make furnaces and then use those to heat metals and work them into desired shapes. And it explains about the materials that have been used to make the furnaces and how they have to tolerate the heat and so on. And then about concrete and the chemistry there (very broadly, this should be about learning about the world not min maxing industrial processes wtf).
Anyone got anything? I do have a book about experiments and I looked through it a bit and it seems cool, like they point out things like you can’t have a conical flask without a permit in Texas because they are afraid of people making meth and so in, and I hope it doesn’t get too autistic and dry but I want more.

Anonymous at Wed, 21 Aug 2024 16:13:03 UTC No. 16336248

>>16335977
is this an engineering book? Terrible argumentation all around

Anonymous at Wed, 21 Aug 2024 16:16:08 UTC No. 16336254

>>16336135
You are never going to find that in a single book. The scope is too vast.

Anonymous at Wed, 21 Aug 2024 16:17:29 UTC No. 16336255

>>16335977
Where in the text is the ordering of the domain used?

Anonymous at Wed, 21 Aug 2024 17:05:51 UTC No. 16336319

>>16336254
I thought it might be so. It’s broad in a way but it’s also more shallow, and also I was hoping for something like a site since it’s easier to just link a video showing the thing, which is vastly better than a word description of a physical thing.

Anonymous at Wed, 21 Aug 2024 17:12:33 UTC No. 16336327

>>16336135
there isn't even a book series besides Landau Lifshitz that treats as much physics and their approach is entirely based on deriving physics from first principles while being extremely concise. If they were to additionally talk about the history of experiments and experiment design, I'd guess it'd quickly go from 5000 pages to 20000.

Anonymous at Wed, 21 Aug 2024 22:06:53 UTC No. 16336811

i was wondering what would happen if i created entangled pair of photons and send one of them into the black hole. if i did that and then observed the one i still have and it had a defined spin, wouldn't this prove that black holes don't destroy information?

Anonymous at Wed, 21 Aug 2024 22:20:54 UTC No. 16336843

>>16336811
That's an excellent question and one we don't have an answer for since it involves the black hole information paradox and quantum gravity. Neither of which are currently understood.

> wouldn't this prove that black holes don't destroy information?
There are arguments for and against if the information is lost or not. There's a comprehensive video covering the topic here: https://youtu.be/Rogm_lpVZYU

Anonymous at Wed, 21 Aug 2024 22:44:40 UTC No. 16336879

>>16336843
it's even hard to test that experimentally because of long i'd have to wait for the photon to finally cross the event horizon from my perspective

Anonymous at Wed, 21 Aug 2024 23:02:01 UTC No. 16336904

>>16336879
You're right. Also strictly speaking we haven't even proved black-holes exist since we haven't been in the proximity to one to directly observe it.

Anonymous at Wed, 21 Aug 2024 23:43:19 UTC No. 16336973

>>16336904
>to directly observe it
Anon is a jokester

Anonymous at Wed, 21 Aug 2024 23:58:34 UTC No. 16336992

>>16336973
Only in part. We have a ton of indirect evidence, but nothing more than that. If people are being pedantic, for example the Nobel Prize committee, the recent award for the observation of the "black hole" at the center of our galaxy never actually mentions the word "black hole" in the entire transcript, not once. It was awarded for confirming the existence of a super-dense compact object. In our current theories we know of no object it could be except for a black-hole - nothing else can be that small and heavy - but like I semi-seriously mentioned, it's still not direct proof.

Anonymous at Thu, 22 Aug 2024 00:08:49 UTC No. 16336996

>>16336992
what i meant is that you can't directly observe a black hole as it doesn't reflect any light. you can really only see the accretion disk
...i thought that you'd pick up on the joke...

Anonymous at Thu, 22 Aug 2024 00:17:46 UTC No. 16337001

>>16336996
I knew what you meant anon. Still worth a reply though.

Anonymous at Thu, 22 Aug 2024 05:09:26 UTC No. 16337280

>>16336327
Im not interested in autistic dry textbook derivations, I just want a rough idea of how the experiments look or what people were doing in the past that yielded that understanding, like how people figured out how to make vinegar by letting wine ferment some more. Like actual real world shit man.

Anonymous at Thu, 22 Aug 2024 07:57:18 UTC No. 16337393

>>16337280
Then you need to read some history of science texts. But even then they wouldn't be general, they'll focus on a particular topic or person.

Anonymous at Thu, 22 Aug 2024 08:14:36 UTC No. 16337411

>>16337393
That is kinda it but I’m only interested in the historic aspect only insofar as it informs what/why we’re doing things as we are today and also as an aid for memory and understanding the world. I’m afraid of them either being popscu drivel or autistic historical books where they go too far into niche detail like what some shot in bumfuck did different from the rest to increase productivity by 0.03% which is not at all relevant when tech advances, e.g. they figured out a billow made with ballsack hair provided 1 degree more heat which reduced the amount of coal.
I want something where I actually feel like I gain a better understanding of the tangible day to day life.
If you got something like that post it. I did find the “how its made” videos on glass interesting cause you actually see glass shaped like that in your home.

Anonymous at Thu, 22 Aug 2024 08:39:10 UTC No. 16337426

>>16337411
>>16337393
>how its made
Which also is a good jumping off point cause they might mention something like glass vs crystal so I can just look it up.
I’ve also been interested in glass working since seeing thunderf00ts video where he makes the glass apparatus he needs for his experiments himself.

Anonymous at Thu, 22 Aug 2024 10:03:24 UTC No. 16337528

https://x.com/cremieuxrecueil/status/1650368177245761539?s=20

Who won this argument about genetics and IQ? I can't tell, both sides think the other one got owned apparently?

Anonymous at Thu, 22 Aug 2024 10:07:13 UTC No. 16337536

>>16337528
The one who lost was most definitely the viewers.

Anonymous at Thu, 22 Aug 2024 12:08:40 UTC No. 16337723

Is there an AI which can make image memes for you if you tell it what to do?

Anonymous at Thu, 22 Aug 2024 12:33:35 UTC No. 16337748

>>16337411
You won't get a good understanding of the historic significance unless you formally study chemistry or something.
A chemistry degree basically walks you through the path of human cognitive development from the 1800's through the 1950's.
Do yourself a favor and just skip that stuff and focus on the past 50 years of compsci.

Anonymous at Thu, 22 Aug 2024 13:16:58 UTC No. 16337800

>>16337748
As I said I don’t care about the history for it’s own sake, but the haber process makes a whole lot more sense with more context around it and the context also adds significance to it making it easier to remember and integrate with other things you know about the world.
A chemistry degree is overkill here, Im basically saying I want to learn how to swim and you’re telling me to enrol into a program for olympic level swimmers.
Many elements in basic chemistry pop up again and again in things you use, silica, lime, soda (baking, washing, caustic, ash), vinegar, iron, carbon. I don’t need a chemistry degree to learn some uses for them, that’s just nonsense.

Anonymous at Thu, 22 Aug 2024 13:32:59 UTC No. 16337821

>>16337800
how does the Haber process make more sense with the historical context?

Anonymous at Thu, 22 Aug 2024 13:37:47 UTC No. 16337828

I want to try out the IMAT exam to attend med school. What are the best ways to prep myself on the physics and chemistry sections of the exam?

Anonymous at Thu, 22 Aug 2024 13:39:46 UTC No. 16337830

>>16337821
Because of how it affected agriculture and how much people land could sustain before and after it. Also ammonia is aso a good degreaser, which you can use to clean clothes and around the house.
Inb4
>that the product and not the process that makes the product
Obviously their interlinked

Anonymous at Thu, 22 Aug 2024 14:19:17 UTC No. 16337890

>>16337830
They’re

Anonymous at Thu, 22 Aug 2024 14:38:34 UTC No. 16337911

>>16337280
Your best bet is to use something comprehensive like Landau as a blueprint for which topics to cover and then look up history books on these individually

Anonymous at Thu, 22 Aug 2024 14:40:30 UTC No. 16337914

>>16337911
Yeah, seems like it. Would be nice if there were something though, like a site about natural phenomena you should be aware of, kinda like a school curriculum that is suppose to prepare you for life bit actually does it

Anonymous at Thu, 22 Aug 2024 14:44:12 UTC No. 16337923

Is the second integral well-defined? Because they're integrating over the domain [math]A[\math], even though e_{a} is not defined in [math]a \in A[\math].

Anonymous at Thu, 22 Aug 2024 14:45:12 UTC No. 16337924

>>16337923
Is the second integral well-defined? Because they're integrating over the domain [math]A[/math], even though [math]e_{a}[/math] is not defined in [math]a \in A[/math].

Stupid formatting.

Anonymous at Thu, 22 Aug 2024 14:47:48 UTC No. 16337925

>>16337924
It doesn't need to be defined at a for you to integrate it. It just needs to be integrable in neighborhood of a.

Anonymous at Thu, 22 Aug 2024 16:15:24 UTC No. 16338033

>>16337925
makes sense thanks

Anonymous at Thu, 22 Aug 2024 21:39:18 UTC No. 16338549

>>16334617
I tried asking this in /his/ but my post was instantly jannied.

I have developed a method to decipher messages which are encrypted with a one time pad. It is a brute force method which only works on very short messages.

Where can I get some old messages to test on? If I open them I will post the results here.

>a spell of anti-jannying
If this post is deleted without explanation, I will just post the code.

Anonymous at Thu, 22 Aug 2024 21:42:05 UTC No. 16338552

I’ve only had 3 hrs of sleep a night for 4 straight nights. Have I done irreversible damage to my health?

Anonymous at Fri, 23 Aug 2024 05:59:05 UTC No. 16339037

>>16338549
https://archive.org/details/hitlerslettersno0000mase

Anonymous at Fri, 23 Aug 2024 06:06:02 UTC No. 16339046

>>16338549
https://ctext.org/analects

Anonymous at Fri, 23 Aug 2024 06:26:05 UTC No. 16339067

>>16338549
> developed a method to decipher messages which are encrypted with a one time pad
> It is a brute force method
thanks for the laugh. try >>>/x/ they'll love you.

Anonymous at Fri, 23 Aug 2024 15:01:47 UTC No. 16339566

>skin color is a mix when different races breed
>every single other trait is either one or the other
God surely works in mysterious ways.

Anonymous at Fri, 23 Aug 2024 15:05:31 UTC No. 16339567

>>16338552
I sleep every other day and I am still kicking

Anonymous at Fri, 23 Aug 2024 19:06:29 UTC No. 16339886

Stupid question, I know, but if you have y=u(1-Mu) and you assume Mu<<1, then you would get u=y(1+My)+... ?
I get that they are using 1/(1-x)=1+x+... but if you do this:
y/(1-Mu)=u and then y(1+Mu) =u
instead of y(1+My)=u
what am I doing wrong? because you can't substitute u with y in the taylor expansion

Anonymous at Fri, 23 Aug 2024 19:08:30 UTC No. 16339891

>>16339886
Just realized I'm mode AYRAN by studying your words under the impression it's a n-body problem and my biosphere is in the center. It tells me what my self is telling myself.

Anonymous at Fri, 23 Aug 2024 19:11:12 UTC No. 16339897

>>16339891
I didn't understand what you said

Anonymous at Fri, 23 Aug 2024 19:32:15 UTC No. 16339921

>>16339886
Your formatting sucks. Is 'Mu' a single variable ([math]\mu[/math]? If not, why are you suddenly switching from Mu to My?

Anonymous at Fri, 23 Aug 2024 19:41:49 UTC No. 16339942

>>16339921
no, M is a constant and y and u are variables. I have y as a function of u and I want to have u as a function of y.
My textbook says that if y=u*(1-M*u), then to first order you get u=y*(1+M*y)+...
but I'm not sure how he gets there, I'm guessing with taylor, but I'm not sure

Anonymous at Fri, 23 Aug 2024 19:49:25 UTC No. 16339958

>>16339942
Honestly it's probably just a typo. You were right the first time.

Anonymous at Fri, 23 Aug 2024 19:52:25 UTC No. 16339965

>>16339958
I don't think it's a typo, they use the formula several times in the textbook

Anonymous at Fri, 23 Aug 2024 19:58:43 UTC No. 16339973

>>16339965
Maybe I'm having a brain fart but given what you wrote I can't see any way to get that book answer.

Anonymous at Sat, 24 Aug 2024 12:41:16 UTC No. 16340752

Would [eqn]C = \frac{1-(r/R)}{[1+(r/R)]^{n-1}} u(x_{0})[/eqn] also work for the inequality in the example section?

Anonymous at Sat, 24 Aug 2024 15:44:29 UTC No. 16341031

what exactly is a symmetry? I'm studying general relativity orbits and my textbook says that the theta coordinate doesn't vary because of the symmetry between the two hemisferes, but how is that different from the symmetry in the coordinate phi? there's the same gravity for every point of phi and yet phi's derivative is different from zero

Anonymous at Sat, 24 Aug 2024 15:46:56 UTC No. 16341032

Why the fuck things that never expire have expiration date?

>find my old box of condoms that I didn't use ever since gf left me for chad
>allegedly expired in 2022 January.
>plastic seal looks the same as always, shit never rots
>open it, the condom looks the same as always, plastic never rots
>put it on, lube is still good
>stroke it as hard as possible with my dry, callous hands
>forgot to pull back the tip for cum
>cum so hard it almost hurt and I thought for sure it will break and point will be proven
>the condom didn't break

If I fucked a woman, that condom would've done a good job of preventing me from ever becoming a chad and a father, so why lie that I must have thrown it away 2 years ago?

And yes, this IS science, I had a hypothesis, and got a negative result.

Anonymous at Sat, 24 Aug 2024 15:56:44 UTC No. 16341059

>>16336254
I've seen dozens of books this past week alone that attempt to do this. They're childrens encyclopedias about science that only talk about experiment

Anonymous at Sat, 24 Aug 2024 15:58:06 UTC No. 16341063

>>16337723
Yes

Anonymous at Sat, 24 Aug 2024 16:02:12 UTC No. 16341071

>>16341032
Spermicide expires and stops working, that would not be visible. The material itself can become porous, again invisible to the eye.

Anonymous at Sat, 24 Aug 2024 16:03:22 UTC No. 16341074

>>16341031
It would help if we knew what equation(s) you were talking about.

Anonymous at Sat, 24 Aug 2024 16:04:13 UTC No. 16341076

>>16341074
It would help, if, fags, stopped making posts here

Anonymous at Sat, 24 Aug 2024 16:05:01 UTC No. 16341078

>>16341076
so what's your excuse?

Anonymous at Sat, 24 Aug 2024 16:08:38 UTC No. 16341086

>>16341078
You were told faggot. Now stop posting

Anonymous at Sat, 24 Aug 2024 16:08:39 UTC No. 16341087

>>16341074
What I mean is, in an orbit around a star, a planet never leaves the equatorial plane. why is that? the reason I've heard is because there's a symmetry between both sides of the theta coordinate.
but wouldn't the phi coordinate be symmetrical as well? how come the planet can spin around a star if phi is symmetric?

Anonymous at Sat, 24 Aug 2024 16:51:16 UTC No. 16341181

>>16341087
Only symmetry I can think of is that the force exerted on the planet from the mass in each hemisphere is identical, giving you a net-zero result. So the planet remains in the same plane.

Anonymous at Sun, 25 Aug 2024 01:26:07 UTC No. 16342529

Wait, so, tell me if I've got this right
Quantum entanglement is basically just the observer effect, through space? Like if you observe particle A, particle B then degenerates?

Anonymous at Sun, 25 Aug 2024 01:27:17 UTC No. 16342532

>>16341032
>latex doesn't expire
hahahaha oh boy, your gf's in for a scare

Anonymous at Sun, 25 Aug 2024 06:00:22 UTC No. 16343306

>>16342529
Yes. Any observation (measurement) collapses the wavefunction / breaks the entanglement, so affecting the state of the system.

Anonymous at Sun, 25 Aug 2024 07:21:22 UTC No. 16343386

>>16343306
niggerbabble
>>16342529
not real, it's about as scientific as "if anon is not at home then he's outside", simple deduction for thing you don't know until you check

Anonymous at Sun, 25 Aug 2024 07:28:48 UTC No. 16343389

>>16343386
this is the stupid question thread, not the stupid answer thread. try a different board smooth brain, science is not for you.

Anonymous at Sun, 25 Aug 2024 07:35:07 UTC No. 16343395

>>16343389
if my brain was smooth I'd believe that quantum mechanics are real

Anonymous at Sun, 25 Aug 2024 12:49:23 UTC No. 16343740

scientists are doing practical applications of superposition in qubits and this moron >>16343386 >>16343395 will insist that it's not a thing
hell, plants and animals use quantum mechanics

Anonymous at Sun, 25 Aug 2024 12:52:13 UTC No. 16343742

>>16343740
>scientists are using technology that doesn't exist
I heard if you concede before your death, you can still go to heaven.

Anonymous at Sun, 25 Aug 2024 12:55:32 UTC No. 16343745

>>16343742
>nature is using phenomenon that doesn't exist because it's evolutionary advantageous and worth investing energy into

Anonymous at Sun, 25 Aug 2024 12:59:54 UTC No. 16343750

>>16343742
They only way to resolve the ultra violet catastrophe is by means of quantization.

Anonymous at Sun, 25 Aug 2024 13:01:34 UTC No. 16343753

>>16343745
>muh nature is using itself
you're a midwit, everything you write is wrong just because you wrote it
>>16343750
or you know, build more precise tools that just work without doing the equivalent of praying to god

Anonymous at Sun, 25 Aug 2024 13:02:08 UTC No. 16343754

Tell me this limit isn't 0, the answer sheet claims DNE but I don't agree, please help

Anonymous at Sun, 25 Aug 2024 13:03:45 UTC No. 16343757

>>16343753
>build more precise tools
read about a quantum state, spin and superposition and stop being a nigger

Anonymous at Sun, 25 Aug 2024 13:12:45 UTC No. 16343765

>>16343757
>learn about a bunch of niggerbabble
replace with "I don't know anything about this particle" and the meaning doesn't change

Anonymous at Sun, 25 Aug 2024 13:23:17 UTC No. 16343783

>>16343753
>or you know, build more precise tools that just work without doing the equivalent of praying to god
You don't need any sophisticated tools to measure black body radiation, silly anon.
>https://www.youtube.com/watch?v=97AqZBjcdUM

Anonymous at Sun, 25 Aug 2024 14:18:02 UTC No. 16343846

How do you prove the converse of the fifth postulate?

Anonymous at Sun, 25 Aug 2024 14:18:58 UTC No. 16343851

>>16343765
>I don't know anything about this particle
but i do, retard

Anonymous at Sun, 25 Aug 2024 14:30:59 UTC No. 16343866

>>16343851
so stop coping with quantum bullshit and be objective then

Anonymous at Sun, 25 Aug 2024 14:31:51 UTC No. 16343867

>>16343866
oh right, you obviously didn't understand. figures

Anonymous at Sun, 25 Aug 2024 14:35:37 UTC No. 16343870

>>16343754
Why do you think it's zero? Start from there

Anonymous at Sun, 25 Aug 2024 17:25:48 UTC No. 16344199

A unit circle is divided into 11 pieces by using four lines in such a way that the area of the smallest piece out of those 11 pieces is as large as possible. What is the area of the smallest piece?

Anonymous at Sun, 25 Aug 2024 17:32:36 UTC No. 16344224

>>16343870
I get pic related, let r go to 0 and the answer will be 0

Anonymous at Sun, 25 Aug 2024 18:37:48 UTC No. 16344450

How would a proof of real number square root existence with the cut property instead of the LUB property go? Is the archimedean property strictly needed in both or any case?

Anonymous at Sun, 25 Aug 2024 18:40:48 UTC No. 16344462

>>16343846
There is a triangle. Use the sum of its angles

Anonymous at Sun, 25 Aug 2024 18:54:29 UTC No. 16344507

The red curve is the curve of y^x = x*y^y. The blue curve is a circle. The x-coordinate of the center of the circle is some positive real number and the y-coordinate is its radius. The circle never intersects with the red curve.

What is the maximum radius of the circle?

Anonymous at Sun, 25 Aug 2024 22:00:43 UTC No. 16344850

Are these lists from the wiki any good? I'm following the mathematics one while doing a bunch of physics on the side but I'm not sure what I'll be missing out on or if there's something else I should be doing with my time instead.
For context, I'll be going to university next year to study math and I want to build a solid foundation on my own before I do that.
https://4chan-science.fandom.com/wiki/Mathematics
https://4chan-science.fandom.com/wiki/Physics_Textbook_Recommendations

Anonymous at Mon, 26 Aug 2024 00:08:32 UTC No. 16344982

>>16336114
Since [math] \Gamma [/math] is cocompact in [math] G [/math], the quotient space [math] G / \Gamma [/math] is compact. With the projection [math] q : G \to G / \Gamma [/math], the set [math] q(U) [/math] is open in the quotient space, and because [math] G / \Gamma [/math] is compact, we can cover [math] G / \Gamma [/math] with finitely many translates of [math] q(U) [/math], say [math] G / \Gamma = q(U) \cup q(g_1 U) \cup \dots \cup q(g_n U) [/math], for some elements [math] g_1, g_2, \dots, g_n \in G [/math]. Then let [math] S = \Gamma \cap (U \cup g_1 U \cup \dots \cup g_n U) [/math]. Since [math] U [/math] is pre-compact and [math] \Gamma [/math] is discrete, [math] S [/math] is a finite subset of [math] \Gamma [/math]. It remains to show that [math] S [/math] generates [math] \Gamma [/math]. Indeed, for any [math] \gamma \in \Gamma [/math], since [math] G / \Gamma [/math] is compact, there is a sequence of elements from [math] S [/math] that, when composed, yield [math] \gamma [/math]. Hence [math] S [/math] finitely generates [math] \Gamma [/math].

Anonymous at Mon, 26 Aug 2024 04:08:49 UTC No. 16345263

is libgen down or something?
can't access it from tor?

Anonymous at Mon, 26 Aug 2024 04:11:47 UTC No. 16345265

>>16344507
infinite

Anonymous at Mon, 26 Aug 2024 06:08:47 UTC No. 16345333

anyone here have experience with the navy nuke program? I start it next year and have heard it's very difficult. you are basically learning 2 years worth of physics, chemistry, and calculus in 6 months. anyone have any tips?

Anonymous at Mon, 26 Aug 2024 06:15:38 UTC No. 16345340

>>16344850
they're bloated like shit and seriously lacking on later topics (you don't have to complete 5 AoPS books before moving onto calc kek). Especially the physics one is terrible: first you slave through a billion garbage undergrad books only to read Landau Lifshitz (and the Sommerfeld lectures for some reason) once you reach grad level, i.e. treat the same topics you've spent an eternity on already but this time properly.
Here's a much more focused list that unironically treats more topics related to physics despite being much shorter: https://sheafification.com/the-fast-track/

The only real perk I see in the fandom list is a way to organize your math and physics books but as a reading list it's about as unpedagogical as it gets

Anonymous at Mon, 26 Aug 2024 08:24:22 UTC No. 16345475

>>16343754
>>16343870
>>16344224
Still waiting for an answer, I thought about using l'hopital but this isn't a 0/0 scenario

Anonymous at Mon, 26 Aug 2024 08:57:58 UTC No. 16345505

>>16344224
>>16345475
You can show that the limit has two different values depending on the path you take. Try the line [math]y=x[/math] and the curve [math]y = x^{2/5}[/math]. Since this is the case then the limit DNE.

Anonymous at Mon, 26 Aug 2024 10:18:08 UTC No. 16345562

>>16345505
I also found a solution like that with 4/11, how come polar coords fails here?

Anonymous at Mon, 26 Aug 2024 10:33:51 UTC No. 16345571

>>16345562
It isn't given you the entire story, no method works in all situations. Using polar coordinates here is the same as approaching the limit along the line [math]y = kx[/math].

Anonymous at Mon, 26 Aug 2024 10:41:54 UTC No. 16345574

>>16345571
I see, thanks for clarifying.

Anonymous at Mon, 26 Aug 2024 17:58:08 UTC No. 16346160

Brainlet with micropenis here: I was told that Wu experiment (whatever it is) proves that G_d plays dice and that the dice are loaded. Would someone explain it to me?

Anonymous at Mon, 26 Aug 2024 18:35:16 UTC No. 16346253

>>16346160
The experiment showed that a particular particle decay did not behave as expected. It was proof that a previously sacrosanct conservation law had been broken and it took new physics to explain the result, that eventually set the stage for the creation of the Standard Model. It has absolutely nothing to do with dice (probability).

Anonymous at Tue, 27 Aug 2024 06:36:59 UTC No. 16347390

Can outliers point put that something else might be going on if you have a small sample size? Or are they always considered to be erroneous data?

Anonymous at Tue, 27 Aug 2024 09:10:23 UTC No. 16347448

does fapping make ur dick longer or shorter?

Anonymous at Tue, 27 Aug 2024 09:19:13 UTC No. 16347457

>>16347390
They should only be considered erroneous if you have a good reason to believe so (e.g. measurement error). Don't just ignore them because "they complicate things."
Usually (in economic data, for example) it indeed indicates that "something else is going on."

Anonymous at Tue, 27 Aug 2024 16:52:02 UTC No. 16347820

>>16334617
How do we know that the highlighted sets are open?

([math]\gamma_1[/math] and [math]\gamma_2[/math] are different parametrizations of the same manifold)

Anonymous at Tue, 27 Aug 2024 18:06:54 UTC No. 16347901

Bump >>16347820

Anonymous at Tue, 27 Aug 2024 21:18:45 UTC No. 16348206

Supposed that [math] a^n,\ a^{-n}=\tfrac{1}{a^n} [/math] is defined for normally [math] a\in \mathbb{R}, n \in \mathbb{Z} [/math]. It is known that [math] (1+a)^n = \displaystyle \sum_{i=0}^n \tfrac{n!}{(n-1)!} \tfrac{a^i}{i!} [/math]
We don't know what [math] a^x [/math] for any [math] a, x [/math] is.

Let [math] \displaystyle e^x \equiv \sum_{n=0}^\infty \tfrac{x^n}{n!} = \tfrac{1}{e^{-x}} [/math], where [math] x \in R [/math]. It can be shown that [math] \forall x,y \in R,\ e^{x+y} = e^xe^y [/math] and [math] n \in \mathbb{Z},\ (e^x)^n = e^{xn} [/math]. The output of e^x is onto every number in [math] (0,\infty) [/math] and is one-to-one.

Let [math] \ln x [/math] be defined by [math] e^{\ln a} = a [/math], so it's output is uniquely onto every real number. From these properties, [math] e^{n\ln a} = (e^{\ln a})^n = y^n [/math] if n is an integer.

>The Question
But how do you get [math] a^x = (e^{\ln a})^x = e^{x\ln a} [/math] for any x? Or how would you get that [math] e^{xy} = (e^{x})^y = (e^{y})^x [/math] for any x,y?

I have my own ideas, but idk for sure. How does one prove this? I don't think you can simply set it to be true, because it needs to also fit stuff like 2^3 = 8 when you plug em in the series (which of course is true, but it needs a proof, which is basically equivalent to my question).

Anonymous at Tue, 27 Aug 2024 21:29:08 UTC No. 16348220

Does this work?
[math] \; \; \blacktriangle [/math]
[math] \blacktriangle \; \; \blacktriangle [/math]

Anonymous at Tue, 27 Aug 2024 21:52:50 UTC No. 16348244

>>16348220
you're almost there

Anonymous at Tue, 27 Aug 2024 21:54:55 UTC No. 16348250

I've heard that plastic junk takes thousands of years to decompose. Tens of thousands of years from now, what is it going to look like? If people of the far future (humans or aliens) start digging up these ancient landfills, what will they find? Will it all be dirt at that point?

Anonymous at Tue, 27 Aug 2024 21:57:25 UTC No. 16348254

>>16348220
[math] \; \; \blacktriangle [/math]
[math] \blacktriangle \; \blacktriangle [/math]


born to late to properly triforce...

Anonymous at Tue, 27 Aug 2024 22:28:22 UTC No. 16348292

>>16348206
or maybe you can set it to be true actually, idk

Anonymous at Tue, 27 Aug 2024 23:48:06 UTC No. 16348379

>>16348206
it's justifiable because you can show that if it's true, then a^x = a^y -> x = y and x < y -> a^x < a^y from the properties of ln(x) and e^x

Anonymous at Tue, 27 Aug 2024 23:51:09 UTC No. 16348383

>>16348250
glass, bone, and non-rusting metals will remain where conditions are not too acidic

Anonymous at Wed, 28 Aug 2024 00:20:52 UTC No. 16348407

Why isnt fat used as a fuel source for cars etc? Is it just too inefficient that despite it being abundant its not worth it?

Anonymous at Wed, 28 Aug 2024 01:37:34 UTC No. 16348476

>>16348206
>I don't think you can simply set it to be true
You kind of do just set it it to be true. [math]a^x := \exp(x\ln(a))[/math] is exactly what babby Rudin's definition is.
It's the correct definition because you can prove it from scratch for rational x, and then you're just filling in the irrational values continuously, which is the only thing you can do if you want to get a continuous function back

Anonymous at Wed, 28 Aug 2024 03:42:19 UTC No. 16348640

>>16347820
>book assumes manifolds are subsets of R^d
why even do that? you literally strip manifolds of all their usefulness by going back to that 1800s definition

Anonymous at Wed, 28 Aug 2024 03:54:51 UTC No. 16348647

>>16348476
Why are the square roots of -1 or even 1 or 0 important, and how much of an importance are they? Imaginary numbers, dual numbers, quaternions, any Clifford Algebra, why is the sqrt root of a real number important at all? Even something like the 2x2 matrix [ 0 -1 | 1 0 ] when squared becomes the identity matrix [ 1 0 | 0 1 ], so it’s a sort of sqrt of -1 for 2x2 matrices. Is it somehow related to something like apply an operation n times and you end up at the same spot? Then why these stuff often related to applying them twice? Why aren’t cube roots of numbers 0 as important?

Anonymous at Wed, 28 Aug 2024 03:55:59 UTC No. 16348648

>>16345333
the stuff is really basic honestly but if you're unsure if you're going to manage just learn some stuff now

Anonymous at Wed, 28 Aug 2024 04:01:28 UTC No. 16348652

>>16348476
>>16348647
Sorry didn’t mean to tag. I just clicked on it to write a comment without going to the top of the page (I’m on a phone) and forgot to delete the auto >>

Anonymous at Wed, 28 Aug 2024 04:07:38 UTC No. 16348655

>>16348476
Exactly, all irrational points are accumulation points of Q so considering the limits approaching these points is the natural thing to do for extending something to R. Not sure if there's another way to construct it

Anonymous at Wed, 28 Aug 2024 04:41:42 UTC No. 16348681

Given the differential equation, d^2y/dx^2 = - y, how does one possibly glean the idea that the solution is at all related to rotating around a circle? They just don't seem related to me

Anonymous at Wed, 28 Aug 2024 05:07:46 UTC No. 16348695

>>16348681
[math]y''=-y[/math]
[math](-1)y''=(-1)y[/math]
[math]-y''=y[/math]
then by the first, [math](y'')''=(-y)'' = y[/math]
so [math]y^{(4)}=y[/math]
at that point it should be obvious that you're rotating SOMETHING

Anonymous at Wed, 28 Aug 2024 06:41:56 UTC No. 16348787

>>16348695
you can say the same thing about y' = -y, but e^-x is only tangentally related to a circle. All of em involve rotations tangentally, but what singles out the original one asked?

Anonymous at Wed, 28 Aug 2024 06:58:29 UTC No. 16348799

>>16348787
>e^-x is only tangentally related to a circle
It's very much related if you consider complex values.
The only reason why [math]e^{x}[/math] and [math]e^{-x}[/math] stand out when you limit things to the reals is that differentiating them corresponds to 0- and 180-degree rotations, respectively, which can just as easily be interpreted as the identity and a reflection about the axis.

Anonymous at Wed, 28 Aug 2024 07:01:26 UTC No. 16348802

>>16348799
>which can just as easily be interpreted as... a reflection about the axis.
*again, when we are limiting things to the real line

Anonymous at Wed, 28 Aug 2024 08:49:17 UTC No. 16348910

Bump >>16347820

🗑️ Anonymous at Wed, 28 Aug 2024 08:57:02 UTC No. 16348923

[math]U^{OK}_1[/math]

Anonymous at Wed, 28 Aug 2024 13:09:04 UTC No. 16349231

Let [math]A[/math] be a distribution and let [math]\varphi[/math] be a test function. Does [eqn]\int_{\mathbb{R}} dx\, A\left[y \mapsto \varphi(x-y)\right] = A\left[y \mapsto \int_{\mathbb{R}}\, dx\, \varphi(x-y)\right][/eqn] hold?

I think it's true for regular distributions, because you can use Fubini's theorem. But I'm not sure about singular ones.

Anonymous at Wed, 28 Aug 2024 13:12:18 UTC No. 16349236

>>16348910
stop being obnoxious. You even made a fucking thread about it. This is probably the 5th time your shitty calc book is missing critical information and you're asking anons to fill it in. Just read a normal book on differential geometry and stop being a hipster

Anonymous at Wed, 28 Aug 2024 15:46:39 UTC No. 16349423

i dont believe in the gambler's fallacy

Anonymous at Wed, 28 Aug 2024 17:08:31 UTC No. 16349521

is it possible to cut my voice box(losing my ability to speak) without damaging any major arteries?

Anonymous at Wed, 28 Aug 2024 17:22:26 UTC No. 16349527

[eqn]\int_{\mathbb{R}^{2}} d^2\mathbf{x}\, e^{-i\phi}\, \big(\nabla \cdot F\big)[/eqn]Can you do something to simplify this? Assume that \F is a two dimensional vector field defined with \rho and \varphi.

Anonymous at Wed, 28 Aug 2024 17:47:38 UTC No. 16349577

How do I cure my cold?

Anonymous at Thu, 29 Aug 2024 14:59:19 UTC No. 16351094

>>16349577
masturbate

Anonymous at Thu, 29 Aug 2024 15:27:48 UTC No. 16351125

Im trying to recreate a part in CAD and it has this partial cut-out of a circle in it that looks like pic related. Long story short I need to know the radius of this circle. I know theres a formula involving a chord that can give you the radius of a circle where you have less than half of the circle to actually measure, but dont remember what it is.(I've had this exact problem in the past and someone posted a picture with annotations written in russian that could be solved to get the radius, but due to a hard drive failure I dont have the picture anymore)

Pic related is basically what I have to work with. Any ideas?

>>tldr: How do I find the radius of pic related? (where you can only measure the solid parts)

Anonymous at Thu, 29 Aug 2024 15:34:17 UTC No. 16351129

>>16351125
assuming you can measure everything pertaining to the solid bit, then you can find [math]A,B,X[/math] and use the intersecting chords theorem: [math]AB=XY[/math]
https://en.wikipedia.org/wiki/Intersecting_chords_theorem

Anonymous at Thu, 29 Aug 2024 16:30:34 UTC No. 16351200

>>16348640
? How are you defining it then? It's how do Carmo does it. Wikipedia too. If you define it as a parametrized differential map, he argues against it, even though that's how older people did it, so he says.

Anonymous at Thu, 29 Aug 2024 16:40:36 UTC No. 16351215

>>16351200
*differentiable

Anonymous at Thu, 29 Aug 2024 16:43:59 UTC No. 16351221

>>16351129
Thats a good idea. Probably easier than what I worked out.

The idea is you know the chord length L, you can measure from its mid point perpendicular to point f, draw another chord H = fb, then draw a line from the mid point of and perpendicular to H to point k. Then extend lines kg and fe until they intersect at point c which should be the center point of the circle. You can then just measure the length of either of those two lines.

Anonymous at Thu, 29 Aug 2024 16:47:01 UTC No. 16351231

If we are looking into the past when observing other galaxies, is it possible that some planets have life at this moment?

Anonymous at Thu, 29 Aug 2024 16:49:28 UTC No. 16351238

>>16351231
Yes. Both when the light left the stars/galaxies that we are only just now receiving many years later, or also now (from our reference frame) when we are receiving the light, where its possible that those same planets have life on them now (again, from our reference frame) but did not when the light we are currently receiving left them.

Anonymous at Thu, 29 Aug 2024 16:50:04 UTC No. 16351239

>>16351231
Do we have senpai?

Anonymous at Thu, 29 Aug 2024 17:30:35 UTC No. 16351308

Is it true and if so, why? The iota is the inclusion of the distributions into the dual of the Schwartz space.

Anonymous at Fri, 30 Aug 2024 02:47:17 UTC No. 16352081

I was thinking about space elevators and I'm not convinced they work anymore. How do you keep the satellite in orbit? I get how the elevator is supposed to work, but once you have a weight on the end of the cable logically it would pull the satellite down and in order to correct its orbit it would need to expend energy to exactly offset the force of that weight. To my mind that means that you still require the same amount of energy to raise a body into orbit. I've seen designs that use a counterweight on the space side of the elevator, but you'd need to expend energy to keep the weight above the satellite since it's not in a real orbit and you'd need an even stronger material than the elevator cable to handle all the stresses.

Am I stupid or something? I refuse to believe I'm the first person to think of this problem, so it's either been solved or it's not actually a problem for some reason.

Anonymous at Fri, 30 Aug 2024 02:58:09 UTC No. 16352090

>>16352081
how could you miss the centrifugal force?

Anonymous at Fri, 30 Aug 2024 03:04:23 UTC No. 16352097

>>16352090
The centrifugal force is factored into the orbit unless you have a counterweight, but like I said, if you have a counterweight then you need to expend a bunch of energy to keep it above the satellite in a forced orbit or it tears the whole structure apart.

Anonymous at Fri, 30 Aug 2024 03:13:45 UTC No. 16352111

>>16352097
no, look. part of the cable that's most affected by the gravity pulls down. the top part along with the elevator and weight pulls away as they try to escape. the cable is being pulled from both sides, the tension is preserved and everything is fine
take a thread, attach some weight to one end and spin it by the other end, see for yourself
the only problem is material strong enough to survive this

Anonymous at Fri, 30 Aug 2024 04:25:22 UTC No. 16352167

>>16352111
You're completely missing the point. What you described is a static situation with all the forces balanced. As soon as you put something in the elevator the forces are unbalanced and that weight is now supported by the cable which pulls on the satellite pulling it out of orbit. In order to compensate the satellite needs to burn fuel equal to the force it sees from the elevator.

Anonymous at Fri, 30 Aug 2024 04:34:52 UTC No. 16352174

So if you observe a particle in the two slit experiment, the wavefunction degenerates, right? And an "observer" is just any detector that interacts with the particle?

Doesnt that include air? Shouldnt air also be capable of interfering with particles? Do all these experiments have to be done in a vaccuum?

Anonymous at Fri, 30 Aug 2024 04:46:25 UTC No. 16352185

>>16352167
>with all the forces balanced
but forces don't need to be balanced. the satellite will pull with extra force and earth is too massive to be visibly affected

Anonymous at Fri, 30 Aug 2024 04:46:32 UTC No. 16352186

>>16352174
An "observer" is a measurement, which is any particle interaction that causes a change in energy. So yes, any collision with an air molecule would collapse the wavefunction. However you can still perform the experiment. Just send through a lot of particles and enough will reach the detector without any other collision. The generated interference pattern though will just have more noise than if you had used a vacuum.

Anonymous at Fri, 30 Aug 2024 04:49:44 UTC No. 16352192

just trying to understand standard deviation. So I have a var(x) value of .96 and the std to be .98, should the std value be near the var(x) value?

Anonymous at Fri, 30 Aug 2024 04:54:16 UTC No. 16352196

The exponential map takes in a point on a surface and a tangent line passing through the point, and maps that line to a geodesic passing through the point whose initial tangent is parallel.
From the surface tangent to that point, instead of a tangent line, supposed the exp map is given a circle centered at that point. Why is the mapped circle also a geodesic (called a radial geodesic)? I feel this came out of nowhere

Anonymous at Fri, 30 Aug 2024 04:56:35 UTC No. 16352198

>>16352185
You have no idea what you're talking about.

Anonymous at Fri, 30 Aug 2024 04:56:55 UTC No. 16352199

>>16352192
Variance is the square of the standard deviation, no?

Anonymous at Fri, 30 Aug 2024 05:15:48 UTC No. 16352211

>>16352198
Anon, why don't you take a weight on a thread, spin right round and see for yourself?
try different weights and speeds, attach one extra in the middle, cut the thread while you're spinning. put a ring near your end and let it loose, see how it behaves

Anonymous at Fri, 30 Aug 2024 05:27:59 UTC No. 16352217

>>16352199
Yes. I'm just trying interpret what the numbers mean/indicate

Anonymous at Fri, 30 Aug 2024 05:53:48 UTC No. 16352226

>>16352217
well .98 * .98 = .96, idk what you mean by asking should they be near each other. 10*10 = 100, or 0 * 0 = 0, or 1*1 = 0. Sometimes x^2 ~ x, and sometimes it aint.

If ur asking for meaning, just look at its equation. Variance is the ave squared distance to the mean. On the other hand, the average distance from the mean is 0 (that's the def of a mean). Asking something like that is sorta useless, so variance is used instead. You could ask why the absolute value of the distance isn't used instead - and it exists - but variance is nicer to do math with. You get analogous stuff to a^2 + b^2 = c^2. Standard deviation square roots the entire thing so it has units we can understand.

It's like how you got mean, median, and mode to describe "center". You also got variance, standard dev, and |distance| to describe "how far from the center".

Anonymous at Fri, 30 Aug 2024 06:22:15 UTC No. 16352239

>>16352196
ignore this

Anonymous at Fri, 30 Aug 2024 11:08:11 UTC No. 16352460

Is the sound reduction of a material purely dependent on its mass? Would a wall of wood that weighs 100kg and is 10cm thick block as much sound as a denser wall made of metal that is 100kg and 5cm thick?

Anonymous at Fri, 30 Aug 2024 11:36:50 UTC No. 16352496

So gravity has got to be handled by a particle, yes? What if it isn't, though? What would be the consequences for particle physics?

Anonymous at Fri, 30 Aug 2024 11:53:24 UTC No. 16352517

>>16352496
Nothing at all, it would just mean that gravity is not a quantum field.

Anonymous at Fri, 30 Aug 2024 13:36:08 UTC No. 16352602

If you poop in space and proton decay doesn't happen, what is the fate of your poop in the heat death of the universe?

Anonymous at Fri, 30 Aug 2024 14:05:07 UTC No. 16352635

>>16352211
Why don't you tie a weight to a balloon and see if it goes up or down? You have no idea what you're talking about.

Anonymous at Fri, 30 Aug 2024 14:06:36 UTC No. 16352638

>>16352460
No

Anonymous at Fri, 30 Aug 2024 14:12:40 UTC No. 16352649

>>16352602
no

*confronts you*

Anonymous at Fri, 30 Aug 2024 14:47:10 UTC No. 16352694

>>16352635
i can't help you if you lack elementary knowledge to understand basic concepts. just accept that it works and trust scientists
if you're still insisting on knowing then read this section
https://en.wikipedia.org/wiki/Space_elevator#Physics and make sure to not skip any references

Anonymous at Fri, 30 Aug 2024 15:27:38 UTC No. 16352727

>>16352081
The answer to your question is the strength of the material.

You have an net force [math]F_C[/math], which is exerted on the structure away from earth. The strength of the material prevents it from being hurled off into space. If you now pulled up a mass [math]m[/math] and if approximately [math]F_G = m g \ll F_C[/math], then the structure would not fall down or move at all. However, [math]F_C[/math] would in fact be reduced. So you'd have to watch out for what masses and how many you simultaneously pull up.

Anonymous at Fri, 30 Aug 2024 18:44:23 UTC No. 16352949

If you uniformly pick two random points inside a semi circle and draw a line through the points, what is the probability that the line intersects the bottom edge of the semi circle?

Anonymous at Fri, 30 Aug 2024 19:17:45 UTC No. 16352998

>>16352949
i don't want to calculate this but it must have something to do with one of the points being located inside the triangle and the line being at an angle greater than alpha, in relation to the diameter

Anonymous at Fri, 30 Aug 2024 19:21:44 UTC No. 16353003

>>16352998
fuck you 4chin for trying to block my picture

🗑️ Anonymous at Fri, 30 Aug 2024 19:34:05 UTC No. 16353019

how can I know that this universe is real

Anonymous at Fri, 30 Aug 2024 19:35:18 UTC No. 16353021

>>16353019
By eliminating all the non-fags until there was just you left and then knowing that you need a universe

Anonymous at Fri, 30 Aug 2024 19:36:47 UTC No. 16353024

>>16353019
please ignore this schizopost and keep discussing actual /sci/ topics

Anonymous at Fri, 30 Aug 2024 19:38:00 UTC No. 16353027

>>16353019
take 1mg of LSD

Anonymous at Fri, 30 Aug 2024 20:12:53 UTC No. 16353070

>>16352727
You're also missing the point. The strength of the material is immaterial. It could be infinite for all I care. How does the satellite stay up. Orbits are very delicate things that are very easy to disrupt. When you put a force on a satellite it is knocked out of orbit. To compensate for this you need to put an equal force in the opposite direction. If you have a satellite lift an elevator then that elevator puts a force on the satellite that must be compensated for. You have only succeeded in moving your rocket motor from the ground to geosynchronous orbit, but you still need the rocket motor.

Anonymous at Fri, 30 Aug 2024 20:14:26 UTC No. 16353073

>>16352694
>It just werks!
I read your posts and you do not get to talk down to anyone about physics.

Anonymous at Fri, 30 Aug 2024 21:02:03 UTC No. 16353127

>>16353070
>Orbits are very delicate things that are very easy to disrupt
see, Anon, you don't even understand this bit correctly. how is anyone supposed to explain anything if you refuse to listen. did you even bother clicking that Wikipedia link?
>>16353073
yes, it just does. what else is there to say?

Anonymous at Fri, 30 Aug 2024 21:42:17 UTC No. 16353193

>>16353127
here, i made a 1000 hours in mspaint presentation just for you. i hope this helps

Anonymous at Fri, 30 Aug 2024 22:04:28 UTC No. 16353215

>>16352081
>To my mind that means that you still require the same amount of energy to raise a body into orbit.
well yea, no one was claiming that space elevators were free-energy machines, but you can use the rotation of the earth to power the horizontal part of the ascent. you still have to power the vertical part yourself tho.
assume the mass of a space elevator is 100% concentrated at the top (big ol counterweight). if the mass is exactly at the geostationary orbit altitude (~32,000 km iirc), then theres no tension in the rope. after the mass moves up past that point, it naturally wants to lag behind in its orbit, but once that happens the tension in the rope is pointing (partially) in the direction of the mass's velocity (pic related; in math terms we would say that the dot product of the velocity and the force is nonzero), so the earth begins doing work on the mass which causes it to speed up in its orbit until the rope is pointing directly upwards. now theres tension in the rope that keeps the mass from flying off, but the mass is otherwise not gaining or losing energy. the energy required to speed the mass up came from the earth; the earth is now rotating a tiny bit slower. if the mass drops a bit (still above geostationary), the opposite happens: the mass pulls ahead in its orbit, rope slows it down, earth speeds up a bit. think of a figure skater pulling her arms in to spin faster.
once the tension is high enough to send an elevator up, youve made a space elevator. the tension creates a negative feedback that keeps the rock in place: rock drops down -> rock speeds up -> rock leads earths orbit -> rope slows it down -> rock lags earths orbit -> rope speeds it up -> rock moves back up.
every time you send mass up the elevator, youre *technically* stealing energy from the mass, but not a way that causes it to drop, but rather youre causing the earth (and therefore the rock) to spin a little slower.

Anonymous at Fri, 30 Aug 2024 22:33:52 UTC No. 16353230

>>16353215
>horizontal part of the ascent.
NTA but what does that even mean?

Anonymous at Fri, 30 Aug 2024 22:35:54 UTC No. 16353235

>>16353230
in order to put yourself in orbit, its not enough to just go up, you also have to go sideways. did you think the ISS orbited the earth at 5 miles/second just for fun?

Anonymous at Fri, 30 Aug 2024 22:40:57 UTC No. 16353243

>>16353235
we're talking about the elevator here. you can only go up the cable
the horizontal speed and angular momentum are a different matter

Anonymous at Fri, 30 Aug 2024 22:43:50 UTC No. 16353246

>>16353243
going up the cable requires increasing your horizontal velocity. if you dont understand this then at present i dont think youre capable of understanding how space elevators work.

Anonymous at Fri, 30 Aug 2024 22:45:03 UTC No. 16353248

>>16353246
except you don't have to do anything because rope does it for you as it pulls you along, smartass

Anonymous at Fri, 30 Aug 2024 22:48:04 UTC No. 16353252

>>16353248
lol i guess you do understand how space elevators work. so, to recap, my original post said
>you can use the rotation of the earth to power the horizontal part of the ascent
which you didnt seem to understand, however, you now say
>you don't have to do anything because rope does it for you as it pulls you along
so cool, we're all on the same page, k?

Anonymous at Fri, 30 Aug 2024 22:53:52 UTC No. 16353257

>>16353252
i just don't get what this horizontal ascent could possibly mean but okay, semantics. my bad

Anonymous at Fri, 30 Aug 2024 23:40:09 UTC No. 16353289

Is Geology a real science or is it just people too dumb to do theoretical physics using math to do surveying work?

Anonymous at Sat, 31 Aug 2024 00:12:52 UTC No. 16353341

>>16353193
That design will tear itself apart unless you have a rocket motor on the counterweight. You've only succeeded in moving the rocket motor from the satellite to the counterweight.

Anonymous at Sat, 31 Aug 2024 01:51:48 UTC No. 16353450

There is not a single subject I've encountered so far that was more demoralizing than analysis. Reading Abbott (the EASIEST book) is still too difficult. You have to constantly pretend you don't know what you already know (hey let's pretend sqrt(2)^2 > 2), and you never know whether a proof is correct since you can't check it or simulate it like in EE. I'm just constantly worried whether I've learned anything whatsoever.
>>16352949
It's the average area of gray for all points inside the circle / area of circle

Anonymous at Sat, 31 Aug 2024 02:38:32 UTC No. 16353503

How do I make friends as a math nerd?
The university refuses to give me any social jobs like tutoring or TA'ing because they are reserved for the le hecking precious prefect baby PhDtards
today one of them didn't even understand linearity. But ooo I'm a le master's student I'll be out of there soon and have a le job so who cares about me might as well not even include le untouchable master's students on the emailing list.
Apperently they've been throwing these social parties with the PhD and undergraduate students from math, engineering, and data science and I just found out that some guy who looks 30 and divorced in my class is now dating a first year undergrad. Wtf?
This is ridiculous and unfair.
I didn't have a good time socially in my undergrad either, and now it's continuing. And I can't even relieve my sexual frustrating because my apartment walls are paper thin... but that doesn't stop the neighbors from screaming like retards at 2am.
Fuck, my life is fucking awful, it's like I'm in hell. This is somehow worse than my undergrad. At least I could jerk off and sleep in peace. The other master's students just seem like zombies. They don't talk, they just go through the motions like they don't even care about being alive.
I rejected some very prestigious PhD programs to get a master's at a good university to get a job so I can support my family financially. I just think it would be nice to at least have one thing. Apparently most the PhS students made a discord server where they just blatantly cheat. I overhead them talking about it. This is just fucking bullshit. I'm starting to get really jaded with the world. I don't even want to be part of this society, it's so fucking stupid, immoral, and unfair. Why would I want to be part of that?
So yeah I dunno my first semester of graduate school isn't going so well. Wondering if you guys ever felt the same way? I mean I was told that going to grad school meant I was going to be around people more like me, but no

Anonymous at Sat, 31 Aug 2024 03:18:16 UTC No. 16353552

>>16353341
why would you ever need a rocket motor? for what purpose?

Anonymous at Sat, 31 Aug 2024 04:01:32 UTC No. 16353583

>>16353552
A forced orbit requires energy to maintain.

Anonymous at Sat, 31 Aug 2024 04:30:23 UTC No. 16353595

>>16353583
no. no, it does not. you would know this if you bothered to read the wiki article

Anonymous at Sat, 31 Aug 2024 09:43:58 UTC No. 16353851

>>16334617
Let's say I have an arbitrarily shaped mirror modeled as a 2D surface and I illuminate it with a point-like light source in arbitrary location.
How can I find the location of the virtual image of that source, if there is any? Should I test infinitely many rays and check whether the continuation of the reflected rays behind the mirror intersect in one point?

Anonymous at Sat, 31 Aug 2024 10:10:30 UTC No. 16353876

>>16353503
>tutoring
>reserved
stop relying on uni and go off campus

Anonymous at Sat, 31 Aug 2024 10:15:41 UTC No. 16353880

>>16352460
No. Not sure about the exact relation, but it also depends on the speed of sound in the material and the cross-sectional length a standing wave would have to go through to attain a standing wave.

Anonymous at Sat, 31 Aug 2024 10:54:10 UTC No. 16353899

I got pic related to store IPA when cleaning electronics and stuff, should I be worried about peroxide formation?

There's one study below where similar plastic contaier created peroxides after 6 moths and constant light exposure but as always lab and real world are two different things.

https://pubs.acs.org/doi/10.1021/acs.oprd.2c00112

Anonymous at Sat, 31 Aug 2024 11:31:28 UTC No. 16353933

>>16353880
It does make sense that sound would have more opportunity to lose energy if it spends more time travelling in a material. Cool that soundwaves can result in so many different patterns

Anonymous at Sat, 31 Aug 2024 13:00:48 UTC No. 16354037

>>16353899
nah
first of all, water content tends to slow their formation, and second the explosions only happen when you distill large quantities (100mL+) of it rapidly. for regular application (disinfecting, cleaning residues etc.) it's not a concern.

Anonymous at Sat, 31 Aug 2024 14:13:36 UTC No. 16354164

I heard differential geometry is also used in classical mechanics. I've seen it nowhere when I did my undergraduate mechanics course. Can somebody recommend me mechanics textbooks where they apply it?

Anonymous at Sat, 31 Aug 2024 14:36:29 UTC No. 16354190

>>16354164
> I've seen it nowhere when I did my undergraduate mechanics course.
Not a surprise, that's some very advanced and abstract topics. You're probably describing symplectic geometry as a way to create a different formalism for Hamiltonian / Lagrangian mechanics. I'm not even sure if it has any applications, it's more a mathematical research area.

Anonymous at Sat, 31 Aug 2024 15:02:51 UTC No. 16354230

>>16354037
Thanks, I did some more reading (as chemistry definitely isn't my strongest subject and even if in some very favourable conditions IPA formed peroxide crystals they won't go bang on their own as the reaction needs either pressure or heat to ignition.

Anonymous at Sat, 31 Aug 2024 15:31:52 UTC No. 16354264

>>16353595
It does. That's why it's called a forced orbit.

Anonymous at Sat, 31 Aug 2024 18:48:26 UTC No. 16354415

So who don't AI people use quantum computers to train their models? I thought those were 10 gorillion times faster at doing anything than normal computers

Anonymous at Sat, 31 Aug 2024 19:00:38 UTC No. 16354427

>>16354415
there are no quantum computers as of now. there are only quantum calculators

Anonymous at Sat, 31 Aug 2024 22:46:39 UTC No. 16354715

>>16353876
What do you mean?
I tried doing it online but I was rejected for not having experience in tutoring.

Anonymous at Sun, 1 Sep 2024 01:46:13 UTC No. 16354914

If I could get a hint on this rather than a straight up answer that would be preferable. I've been a little stuck trying to prove if the following is true:
Is [math](\mathbb{R}[x]/\langle x-1\rangle)/\langle \overline{x+1}\rangle\cong \mathbb{R}[x]/\langle x^2-1\rangle[/math] where [math]\overline{x+1}[/math] is the equivalence class of [math]x+1[/math] in [math]\mathbb{R}[x]/\langle x-1\rangle[/math]
Or at the very least one is isomorphic to a (nontrivial) subring of the other. I messed around with the equivalence classes in [math](\mathbb{R}[x]/\langle x-1\rangle)/\langle \overline{x+1}\rangle[/math] but didn't get all that far yet. There is probably some way to apply the isomorphism theorems but I was trying to make the isomorphism/homomorphim myself. This seems like something that could be true. If it's not I'd like a hint on how to disprove this instead

Anonymous at Sun, 1 Sep 2024 01:54:23 UTC No. 16354922

Best place to find books aside from libgen and Anna's archive?

Anonymous at Sun, 1 Sep 2024 01:54:37 UTC No. 16354923

>>16354922
Your local library.

Anonymous at Sun, 1 Sep 2024 01:55:30 UTC No. 16354924

>>16354923
That was too quick of an answer

Anonymous at Sun, 1 Sep 2024 01:59:10 UTC No. 16354926

>>16354924
Your answer to my post was too slow. You are dead. Go find your Drill Instructor and ask for 100 push ups.

Anonymous at Sun, 1 Sep 2024 02:00:32 UTC No. 16354928

>>16354926

Anonymous at Sun, 1 Sep 2024 05:22:07 UTC No. 16355008

Is there any supplement that helps against nightmares?

Anonymous at Sun, 1 Sep 2024 06:06:56 UTC No. 16355029

>>16355008
the #1 cause of night terrors is being too hot at night. use fewer blankets, invest in a fan, turn up the AC, etc.

Anonymous at Sun, 1 Sep 2024 07:24:45 UTC No. 16355061

>>16355029
>turn up the AC
Sucks being a Yuropoor, but I think I really do get more nightmares in summer.

Anonymous at Sun, 1 Sep 2024 08:03:46 UTC No. 16355076

>>16354914
It might be a good idea to examine the zero elements in
[eqn]\mathbb{R}[x]/\langle x-1\rangle [/eqn]
and then
[eqn](\mathbb{R}[x]/\langle x-1\rangle)/\langle \overline{x+1}\rangle [/eqn]

Anonymous at Sun, 1 Sep 2024 12:12:27 UTC No. 16355240

>>16334617
>stupid
Help me Anons, apparently three populations of elementary particles are necessary for some Universe symmetry (parity?) to be broken. Anyone knows more about it?

Anonymous at Sun, 1 Sep 2024 12:15:02 UTC No. 16355243

Am I banned?

Anonymous at Sun, 1 Sep 2024 12:19:56 UTC No. 16355248

>>16355243
yes

Anonymous at Sun, 1 Sep 2024 12:58:22 UTC No. 16355285

>>16334628
> What would happen if I drink gasoline?

Anonymous at Sun, 1 Sep 2024 13:51:12 UTC No. 16355326

>>16334628
a candy bar has 4 times more energy than a dynamite stick

Anonymous at Sun, 1 Sep 2024 14:23:08 UTC No. 16355364

>>16355240
No. Why there are three generations of leptons and quarks is possibly the biggest unanswered question in particle physics.

Anonymous at Sun, 1 Sep 2024 15:44:23 UTC No. 16355413

okay so i have a PDE of the form [math]\mathcal{A} \left[u + \partial u/\partial t \right] = f(u)[/math]

where [math]u=u(x,y,t)[/math], [math]\mathcal{A} = \nabla^4 - \nabla^2 + 1[/math], and [math]f[/math] is a potentially nonlinear function

i can barely into numerical analysis, but i need to discretize and simulate the above PDE
if i let [math]\mathcal{A}_{h}[/math] be the matrix form of the discretized spatial differential operator defined above, after applying a backward euler scheme i have
[math]
\mathcal{A}_{h}\left[u^{n+1} + \left(u^{n+1}-u^{n}\right)/\Delta t \right] - f(u^{n+1}) = 0
[/math]
which turns this into a rootfinding problem. is this the right approach?

Anonymous at Sun, 1 Sep 2024 19:14:04 UTC No. 16355615

If my hody temperature us 36.6 °C and room temperature is 20 °C then can I use a thermoelectric generator to get a bit electricity from it?

Anonymous at Sun, 1 Sep 2024 19:39:50 UTC No. 16355652

>>16355615
yes

Anonymous at Sun, 1 Sep 2024 19:42:37 UTC No. 16355655

>>16355652
>>16355615
https://www.youtube.com/watch?v=n-mKP9E6a6I

Anonymous at Sun, 1 Sep 2024 19:50:51 UTC No. 16355669

what is it called when waves phase in and out like this? i'm trying to find a professional image of said phenomenon for a forum post

Anonymous at Sun, 1 Sep 2024 20:42:51 UTC No. 16355724

Wagyu fat has a melting point significantly below body temperature. How can the animal store this fat?
There are some answers, but they are un-sourced non-explanations that just assumes some preceding condition will give the result.

Anonymous at Sun, 1 Sep 2024 20:56:08 UTC No. 16355739

>>16355008
Cocaine. You won't sleep as much, so fewer nightmares.

Anonymous at Sun, 1 Sep 2024 21:13:00 UTC No. 16355767

I'm 30. Is it dumb to go back and get an engineering degree? I can't afford college though because I'm a burger. I just kinda really want to learn EE with no specific job in mind.

Anonymous at Sun, 1 Sep 2024 21:22:38 UTC No. 16355783

>>16355413
never mind, think i figured it out

Anonymous at Mon, 2 Sep 2024 09:24:10 UTC No. 16356442

Does somebody know how to deduce this equation in GR? I think it has something to do with [math]h\nu=p^0[/math] so maybe you should multiply p by itself, or by the four velocity, but isn't that just 0? p2=-m2, and that's 0 for a photon

Anonymous at Mon, 2 Sep 2024 15:41:10 UTC No. 16356786

What is the name of this shape? Also the flatter versions (i.e. octagonal prism with pyramids on both ends). I feel I like I remember typing it but forgot the name

Forgive me I'm from /vr/

Anonymous at Mon, 2 Sep 2024 17:55:31 UTC No. 16356950

>>16356786
>(octagonal prism with pyramids on both ends)
That would be ›elongated octagonal bipyramid‹.
>name of this shape
Hmm. Logic suggests ›elongated bicone‹, but languages aren't exactly logical.

Anonymous at Tue, 3 Sep 2024 01:07:27 UTC No. 16357639

Here me out now:
How stupid would it be to just
>take out a $500,000 mortgage at 3%
>"buy" a house
>reverse mortgage the house
>invest that $500k in a 10% interest investment account
>use dividends to pay mortgage + NEETbux
Would it work???

Anonymous at Tue, 3 Sep 2024 01:22:48 UTC No. 16357667

>>16357639
Don't you have to be at least 60 to get a reverse mortgage?

Anonymous at Tue, 3 Sep 2024 01:24:25 UTC No. 16357670

>>16357667
Oh
But then it's still a valid retirement plan?

Anonymous at Tue, 3 Sep 2024 01:28:51 UTC No. 16357678

>>16357639
You better have some stellar, top notch, hardcore, suck you off then fuck off, A-1, business class, super duper credit to your name
if you want to get that mortgage in the first place.

Anonymous at Tue, 3 Sep 2024 01:30:34 UTC No. 16357680

>>16357670
well you have to own the house first, but yes, it's a way to instantly access the full current value of your home. there's a lot of fine print / details in the arrangement though.

Anonymous at Tue, 3 Sep 2024 01:34:03 UTC No. 16357686

>>16357680
That's what the mortgage is for silly

Anonymous at Tue, 3 Sep 2024 01:35:10 UTC No. 16357690

>>16357686
No, you have to "own" it outright. No existing loan on the property.

Anonymous at Tue, 3 Sep 2024 01:38:03 UTC No. 16357694

>>16357690
Wtf
So there's no other way to financialize a house under mortgage???

Anonymous at Tue, 3 Sep 2024 01:40:58 UTC No. 16357700

>>16357694
You can remortgage it or get a second mortgage.

Anonymous at Tue, 3 Sep 2024 01:43:05 UTC No. 16357707

>>16357700
So free money???

Anonymous at Tue, 3 Sep 2024 01:45:46 UTC No. 16357711

>>16357707
A guaranteed 10% yearly interest return is harder to find than you think, especially one that is tax free.

Anonymous at Tue, 3 Sep 2024 01:48:31 UTC No. 16357714

>>16357711
Even if it's just 5% or 6% that's still "rent" covered
Bruh this is literally free money wtff

Anonymous at Tue, 3 Sep 2024 01:56:41 UTC No. 16357725

>>16357714
And you are still paying off the mortgage, bills, insurance. House prices may fall, interest rates can spike. Nothing is certain.

Anonymous at Tue, 3 Sep 2024 02:12:47 UTC No. 16357747

>>16357725
You are eliminating rent, which for most people is like a 1000% increase in income. You could easily sustain a semi-NEET lifestyle off that
>rates can spike
Fixed rate mortgage wtf

Anonymous at Tue, 3 Sep 2024 02:24:16 UTC No. 16357758

AI didn't consider mortgage a good strategy when playing Monopoly
https://www.youtube.com/watch?v=dkvFcYBznPI
interpret it however you want

Anonymous at Tue, 3 Sep 2024 03:37:07 UTC No. 16357823

My math textbook gives the geometric interpretation of [math]| \vec{a} \times \vec{b} |[/math] as the area of a parallelogram formed by [math]\vec{a}[/math] and [math]\vec{b}[/math], which makes sense if the points of the parallelogram are coplanar. One of the exercises is to calculate the area of a parallelogram given its four points. I guess the idea is to calculate two vectors using the points & to take the cross product of them.

However, when I plot the points they give in a 3D calculator they are most definitely not coplanar and so calculating the area of the 'parallelogram' they give me doesn't seem to make any sense. Are they stupid?

[math]
P=\left(0,0,0\right),
Q=\left(5,-1,5\right),
R=\left(5,0,-6\right),
S=\left(10,-1,-11\right)
[/math]

Anonymous at Tue, 3 Sep 2024 05:05:33 UTC No. 16357890

At the end of the day isn't calculus still just a cope for the inability to divide time down to a single point?
How can we know anything is real if time is infinitely divisible and all things are constantly in motion? Nothing exists at a single point in space at a single point in time and yet that is how we perceive things with our brains

Anonymous at Tue, 3 Sep 2024 07:06:17 UTC No. 16357968

>>16357890
>calculus
>time
Anon, mathematics is infinitely larger than physics. Mathematical abstraction of limit (calculus can be loosely defined as branch of mathematics that deals with limits) doesn't need time to exist.

Anonymous at Tue, 3 Sep 2024 07:32:36 UTC No. 16357995

>>16334617
>stupid
Is Standard Model Turing-complete?

Garrote at Tue, 3 Sep 2024 19:19:45 UTC No. 16358782

How can I integrate
int e^(x^2) dx
?

Anonymous at Tue, 3 Sep 2024 19:25:20 UTC No. 16358799

>>16358782
Write e as its power series, integrate each term separately (which will give you a new series)

Anonymous at Tue, 3 Sep 2024 21:22:48 UTC No. 16358962

>>16358782
EZ way is find the integral of e^(x^2+y^2) and sqrt it

Anonymous at Tue, 3 Sep 2024 21:27:47 UTC No. 16358971

>>16358782
integrate int e^(x^2 + y^2) dx dy on the plane using polar coordinates and then use Fubini and a square root

Anonymous at Wed, 4 Sep 2024 02:33:34 UTC No. 16359474

>>16354914
In [math]\mathbb{R}[x]/\langle x-1 \rangle[/math] you're forcing that [math]x=1[/math]. So, what should the quotient be isomorphic to?

Anonymous at Wed, 4 Sep 2024 02:55:32 UTC No. 16359487

>>16347448
I know for a fact it doesn't get longer.

Anonymous at Wed, 4 Sep 2024 03:20:36 UTC No. 16359503

https://www.researchgate.net/publication/383610584_Experimental_Evidence_of_Possible_Gravity_Modification_based_on_a_Einstein_Unification_Model_The_GEM_Effect
nothing burger?

Anonymous at Wed, 4 Sep 2024 03:42:49 UTC No. 16359514

>>16359503
It's always nothing, and pure schizo babble.

Anonymous at Wed, 4 Sep 2024 10:58:41 UTC No. 16359963

Is there currently any evidence for position or time being fundamentally discrete in the way that energy is?

Anonymous at Wed, 4 Sep 2024 11:21:27 UTC No. 16359987

>>16359963
no

Anonymous at Wed, 4 Sep 2024 12:11:50 UTC No. 16360069

>>16359963
energy is also not discrete.

Anonymous at Wed, 4 Sep 2024 13:55:16 UTC No. 16360185

Let [math]T[/math] be a (bounded) self adjoint positive operator on a Hilbert space such that [math]0[/math] is not an eigenvalue of [math]T[/math]. I'm reading a paper where it's claimed that the spectral theorem furnishes a sequence of (bounded) operators [math](T_n)_{n=1}^{\infty}[/math] such that [math]T_n T \xi \to \xi[/math] for all vectors [math]\xi[/math].

My functional analysis is rusty. How exactly does the spectral theorem imply this? My hunch is to maybe write [math]T = \int_{0}^{\infty} \lambda dE(\lambda)[/math] where [math]E[/math] is a projection-valued measure, and then set [math]T_n = \int_{1/n}^{\infty} \frac{1}{\lambda} dE(\lambda)[/math], say. Am I spewing bullshit here or does this actually work?

Follow-up question: Suppose [math]U[/math] is a unitary that commutes with [math]T[/math]. Does [math]S[/math] also commute with each of the abovementioned [math]T_n[/math]?

Anonymous at Wed, 4 Sep 2024 14:17:25 UTC No. 16360213

>>16357823
Sounds like a sign error in the book. Do it with Q = (5, -1, -5) instead.

Anonymous at Wed, 4 Sep 2024 16:33:05 UTC No. 16360400

I see the x chromosome is unusual, I had some questions about it.

It is always fully expressed in males so bad mutations must be purged readily. Since males only carry one X chomosome a daughter must carry this same X chromosome. Does this imply that a girl is slightly more similar to her father than her mother since her 2 X will be a combination of her mother's two Xs?

If you could line breed a model organism such as a male mouse to its daughters for several generations (perhaps with ai of stored sperm) on average how soon would her two XX be the same as her father's compared to the rest of the genome?

Anonymous at Wed, 4 Sep 2024 16:34:20 UTC No. 16360402

Do you think math is like "working out but for your brain" and everyone should practice it?

Anonymous at Wed, 4 Sep 2024 18:47:12 UTC No. 16360560

>>16355076
I did try to mess with this but I didn't get that far due in part to my pea brain not being sure I set things up right.
What I got looking at the zeros in [math](\mathbb{R}[x]/\langle x-1\rangle)/\langle\overline{x+1}\rangle[/math] was elements that are of the form [math]\overline{p(x)}=\overline{q(x)}\cdot\overline{x+1}[/math] for some [math]\overline{q(x)}\in\mathbb{R}[x]\langle x-1\rangle[/math], which then means [math]p(x)-q(x)(x+1)=r(x)(x-1)[/math] for some [math]r(x)\in\mathbb{R}[x][/math].
What I get out of this [math]p(x)\in\langle x-1,x+1\rangle[/math] which should be an ideal containing [math]\langle x^2-1\rangle[/math] provided I didn't fuck up prior to this.

>>16359474
Yeah, [math]\langle x-1\rangle[/math] is the kernel of [math]\varphi:\mathbb{R}[x]\rightarrow\mathbb{R},\ \ \varphi(p)=p(1)[/math]. [math]\varphi[/math] should be onto [math] \mathbb{R}[/math], so by the first isomorphism theorem [math]\mathbb{R}\cong\mathbb{R}[x]/\langle x-1\rangle[/math].
If I'm interpreting this right, [math]\varphi\langle\overline{x+1}\rangle=\langle2\rangle\subseteq\mathbb{R}[/math],. Since [math]\mathbb{R}[/math] is a field, [math]\varphi\langle\overline{x+1}\rangle=\mathbb{R}[/math] and [math](\mathbb{R}[x]/\langle x-1\rangle)/\langle\overline{x+1}\rangle\cong\mathbb{R}/\mathbb{R}\cong\{\varnothing\}[/math].
I feel like there is some leap in logic here but this is what I got after messing around with it.

I appreciate the suggestions

Anonymous at Wed, 4 Sep 2024 19:01:12 UTC No. 16360575

>>16360402
Math (as in math itself, not just anything that slightly uses math) definitely is a mental exercise, but it isn't the only mental exercise. I do think that everyone should "work out their brain" as much as they are able. With how broad math is I think it's one of the best ways to do so, but there are plenty of ways outside of math to challenge and flex your brain.
Doesn't need to be much either, just a little bit each day is better than nothing. Contrary to what a lot of people on /sci/ over the years have said, not everyone need to be a depressed post-doc turbo autist, but keeping your mind keen is good no matter how you cut it.

Anonymous at Wed, 4 Sep 2024 19:22:46 UTC No. 16360618

>>16360402
You do more to work out your brain, if you do sports. Especially cardio. I don't believe thinking very hard about a math problem is gonna do anything for you. On the other hand I'm not doctor, so not sure. You should ask /med/ about this.

Anonymous at Wed, 4 Sep 2024 20:16:25 UTC No. 16360770

Let [math]K \le H \le G[/math] be groups. Suppose [math]K^h \cap K[/math] has finite index in both [math]K[/math] and [math]K^h[/math] for all [math]h \in H[/math], where [math]K^h = hKh^{-1}[/math].

I'm trying to prove that for every [math]h \in H[/math] there exist finitely many [math]k_1 ... k_n \in K[/math] such that for every [math]k \in K[/math] there is some [math]i[/math] with [math]khK = k_i hK[/math]. It probably amounts to definition-chasing but I haven't made any progress on this problem so I'd appreciate any help

Anonymous at Wed, 4 Sep 2024 21:26:21 UTC No. 16360914

what's the best way to learn calculus 1 as a freshmen for uni? im a dumb dumb and have to take this course instead of calc 3 like my friends because i delayed my progress in high school. is it better to go through a textbook for this or go through online courses / videos to learn? if so, recommend the best for both please

🗑️ Anonymous at Wed, 4 Sep 2024 22:38:34 UTC No. 16361096

>>16360185
T is definitely diagonalizable cuz of spectral theorem, so it can be written as QDQ^{-1}. This means T_{\infty} = QD^{-1}Q^{-1}, where the diagonal of D^{-1} are just 1/{\lambda}, which works cuz there's no zero eigenvalue \lambda. Depending on the value of \lambda, you can write 1/{\lambda} as an infinite sum in the 1/(1-x) infinite series sense, where |x| < 1. Let the sum up to n be QD_nQ^{-1} = T_n. Idk why they using it, but yeah, the sequence of operators def exists. There's prob other ways to make the sequence too but the existence is there.

Idk what S is, but if UT = TU, then yes, UT_n = T_nU. It comes by realizing that DAD^{-1} = D^{-1} A D = A when D is a diagonal matrix with non-zero eigenvalues. You can also show stuff about U^\dagger

Anonymous at Wed, 4 Sep 2024 22:43:56 UTC No. 16361115

>>16360914
textbook is always best. Use youtube+google as a guide when you need help. You need to do the practice problems.

Anonymous at Wed, 4 Sep 2024 23:03:13 UTC No. 16361174

>P(A) =0.5
>P(AUB) = 0.9
What's P(A-B) and why? Yes I am a retard in undergrad probability

Anonymous at Wed, 4 Sep 2024 23:40:58 UTC No. 16361247

>>16360185
T is definitely diagonalizable cuz of spectral theorem, so it can be written as QDQ^{-1}. This means T_{\infty} = QD^{-1}Q^{-1}, where the diagonal of D^{-1} are just 1/{\lambda}, which works cuz there's no zero eigenvalue \lambda. Depending on the value of \lambda, you can write 1/{\lambda} as an infinite sum in the 1/(1-x) infinite series sense, where |x| < 1. Let the sum up to n be QD_nQ^{-1} = T_n. Idk why they using it, but yeah, the sequence of operators def exists. There's prob other ways to make the sequence too but the existence is there.

Anonymous at Thu, 5 Sep 2024 00:00:42 UTC No. 16361299

>>16361174
Draw a venn diagram, i legit learned this in like 4th or 5th grade: two circles overlapping and a rectangle surrounding both. It'll have four sections, where the sum of each section w + x + y + z = 1. Let w be only A, x be A and B, y be only B, and z be neither A nor B.

If .9 represents both circles A and B, what's number goes into section neither A nor B? Since all of circle A should add to .5, what is in the only B section? Can you determine anything else? Obviously not. For the last two sections, you need one more info. This makes sense cuz so far we've only used three equations for four unknowns.

What other information could be used? The most common answer is that events A and B are independent of each other. So FOR EXAMPLE, if P(A) = .4 and P(B) = .2, then P(A&B) = .5 * .2. Or like how if there's a 40% chance it's raining, and a 20% chance I'm hungry, then there's a 8% chance both is true. This is the 4th equation. You're given that all of circle A is .5, you know that the sum A&B + only A = all of circle A, and now you got an extra equation for A&B.

Write all of that in terms of w,x,y, and z. Seriously, just draw the venn diagram picture out.

Anonymous at Thu, 5 Sep 2024 00:10:00 UTC No. 16361322

>>16361299
.4 * .2, not .5*.2

🗑️ Anonymous at Thu, 5 Sep 2024 00:48:58 UTC No. 16361367

>>16360185
I dont see how TU = UT unless the eigenvalues of T are all the same, in which case it's obvious that it works with T_n. Give an example?

Anonymous at Thu, 5 Sep 2024 01:27:29 UTC No. 16361400

>>16360185
If UT = TU, then yes U T_n = T_n U. In fact, U commutes with any matrix with the same eigenvector basis (and the identity matrix).

Anonymous at Thu, 5 Sep 2024 17:54:44 UTC No. 16362452

So, what's a good book for learning the theory behind resonance frequencies for platforms?

Anonymous at Thu, 5 Sep 2024 19:53:01 UTC No. 16362623

>>16334617
I have an 8mm kidney stone in one kidney and a 5 mm kidney stone in one kidney. I take potassium citrate, calcium citrate, drink lemon juice, (all for the kidney stones) and am on other medications (for epilepsy).

The cause of the kidney stones is one of my seizure medications (Topamax). The stones have been stable for many years. I would, however, like to have them pass out of the kidneys. How can I "dislodge" them out of the kidneys?

Anonymous at Thu, 5 Sep 2024 19:57:23 UTC No. 16362636

>>16338549
A "one" time pad can be cracked if someone uses the one time pad more than once.

Also, if the one time pad key is not random, it can also be cracked. For example, if your key is the Declaration of Independence, or if there are full English words, it can be cracked using a crib drag.

Anonymous at Thu, 5 Sep 2024 19:58:54 UTC No. 16362645

>>16362623
you better ask some urologist. preferable methods are sound waves (to break them) or a scope

Anonymous at Thu, 5 Sep 2024 20:15:28 UTC No. 16362674

>>16336135
You might like the books by Vaclav Smil.

Anonymous at Thu, 5 Sep 2024 20:17:32 UTC No. 16362678

hello, i should've stayed late to ask the teacher but i didn't and the test is on tuesday

Finding volume by shell method
Area bound by the curves y = x^3, y = 0, x = 1
Solid formed by rotating about the line y = 1

in class we determined we should put x in terms of y, so x = y^(1/3)

then we determined height as 1 - y^(1/3), and radius as 1 - y

very lost about (1 - y) specifically

🗑️ Anonymous at Thu, 5 Sep 2024 20:34:42 UTC No. 16362716

>>16362678
Draw out the picture and show it to us

Anonymous at Thu, 5 Sep 2024 20:37:33 UTC No. 16362721

>>16362678
Draw out the picture. Where is the center of the solid made of shells? What is the maximum radius of a shell, and what is the y value? What is the minimum radius of a shell, and what is it's y value?

Anonymous at Thu, 5 Sep 2024 20:45:23 UTC No. 16362734

>>16362721
this is the picture

i can understand 1-y^(1/3) but i dont understand 1-y

Anonymous at Thu, 5 Sep 2024 21:24:43 UTC No. 16362772

>>16362678 >>16362734 here
i guess it's just because we're doing it as x in respect to y so we normally do x as the radius by default and so this would be like 1 - x but it's 1 - y, since it's about a line and not the axis. i just gotta read the section and try to understand the formula better so i can wrap my head around what 1 - y represents here

Anonymous at Thu, 5 Sep 2024 21:43:46 UTC No. 16362805

>>16362678
>in class we determined we should put x in terms of y
???
when you integrate, youre adding a bunch of chopped-up volumes together (for this problem, what do the volumes look like?). if the chops go along the x-axis (pic rel, left), then the height of the volumes is dx, so you can just keep is as y=f(x). but if the chops go along the y-axis (pic rel, right), then the height of the volumes is dy, so you can switch it to x=f(y) to help you with your algebra (nb: you dont have to do that, you can integrate with respect to y without swapping anything, but that often confuses students so teachers will often just tell them to swap the variables first).
>how do i know which way the chops go?
they can go anyway you want and youll theoretically get the same answer, but ideally you pick a direction such that the base area of the volumes is easy to calculate; for these revolution problems, picking a direction perpendicular to the axis of rotation usually means that the bases are "donuts", i.e. the area is just the difference between the area of one circle and the area of a smaller circle.

Anonymous at Thu, 5 Sep 2024 21:46:22 UTC No. 16362807

With poo.

I literally know this hylic which can only be understood if you know all the paracols.

Right I might be wrong but I'm intelligent on more than a perfect 'hylic' level.

If I'm wrong I'm wrong. I obviously don't got you in my experience.

Anonymous at Thu, 5 Sep 2024 21:53:34 UTC No. 16362815

>>16362678
>>16362805
oops you said shell method lol, ignore what i said.
please accept this spoon-feed as penance.

Anonymous at Thu, 5 Sep 2024 23:11:23 UTC No. 16362937

What happens if you train an ai/llm off of the greek septuagint version of the biblical old testament?

Anonymous at Thu, 5 Sep 2024 23:16:24 UTC No. 16362947

>>16362815
yea i think for this problem it was just to do shell method for the sake of it, while later on in the section it becomes "decide which one works best and use that"
i just need to understand what the radius represents here in the geometry of the shells and then i'll be okay but i'm having trouble visualizing the cylinders so i can't understand what 1-y is doing
thx for spoonfeed. i'm gonna try to grind some practice problems out tonight but i need to put my desk together and get an espresso

Anonymous at Thu, 5 Sep 2024 23:39:54 UTC No. 16362989

>>16362815
no one make fun of me for fucking this up.
>>16362947
>i just need to understand what the radius represents here in the geometry of the shells
its the radius of the shells. the shells are being created by resolving a surface/"line" around the y=1 line. so if the surface/"line" is located at, say y=0.2, then the radius of the shell is 0.8, and in general r=1-y.
i was a bit verbose in pic related, but instead of adding up a bunch of volumes, you can think of it as adding up an infinite number of areas, which produces a volume. the areas we're adding up are the sides of cylinders, which have an area of A=Ph, where P is the perimeter (circumference). in the final integral, [math]2 \pi (1-y)[/math] is really the perimeter [math]2 \pi r[/math], and [math](1-\sqrt[3]{y})[/math] is the height. you can think of [math]dy[/math] as some magic term that allows the areas to add up to a volume, but technically speaking its the "width" of the cylinders.

Anonymous at Thu, 5 Sep 2024 23:53:46 UTC No. 16363018

>>16362989
:)

Anonymous at Fri, 6 Sep 2024 00:03:23 UTC No. 16363038

I haven't been in school in ages, I seemingly forgot how vector components work - I can't solve the b problem, I'm assuming my setup is wrong I know that you can make it way easier if you use top charge as reference point but I want to to left corner one with regular xy coordinates now that I've gotten stuck so that I can learn what I'm doing wrong:
I've chosen to ignore [math]\dfrac{1}{4\pi\epsilon}[/math] since it won't affect this in anyway the other charges in the vertices are negative because they are equal in charge I.e negative negative or positive positive - to the reference charge
[math]F_{q1_{x}} = \dfrac{Qq}{d^2} \cdot cos(30) - \dfrac{-(q^2)}{3d^2} \cdot cos(60) - \dfrac{-(q^2)}{3d^2} \cdot cos(0) [/math]
Working this out keeps giving me an expression that is always dependent on Q which makes it impossible to solve for Q without Q = 0 which is incorrect.

Anonymous at Fri, 6 Sep 2024 00:08:55 UTC No. 16363045

>>16363038
>Working this out keeps giving me an expression that is always dependent on Q
no it doesnt. set [math]F_{q1_x}[/math] to zero and solve for [math]Q[/math].

Anonymous at Fri, 6 Sep 2024 00:17:25 UTC No. 16363049

>>16363045
Why do I overlook such simple things, I almost shouldn't thank you because that's an insult to your intelligence when all you did was use your eyes. But thanks, in all honesty

Anonymous at Fri, 6 Sep 2024 00:18:28 UTC No. 16363053

>>16363049
you definitely shouldnt thank me since i didnt check if the actual expression was correct ;)
but np fren <3

Anonymous at Fri, 6 Sep 2024 02:06:21 UTC No. 16363161

What am I not getting? I understand the keep, change, flip thing, and how to make an improper fraction. So how can 7/3 become 8/3?

Anonymous at Fri, 6 Sep 2024 02:07:21 UTC No. 16363163

>>16363161
*3/8

Anonymous at Fri, 6 Sep 2024 02:12:01 UTC No. 16363166

>>16363161
typo. [math]2 \frac{1}{4}[/math] is actually less than [math]\frac{7}{3}[/math], so Mac wouldnt even be able to paint a full car as written.

Anonymous at Fri, 6 Sep 2024 02:14:01 UTC No. 16363169

>>16363166
oh, so the chatbot is right?

if so... damn.

Anonymous at Fri, 6 Sep 2024 02:45:27 UTC No. 16363186

>>16337280
I would think some things like the example you provided were discovered purely by accident without any theory or testing anon. Even the creation of wine was likely just a coincidence of fermented fruit juices that someone found with some prior knowledge to what it was and realized something had happened to it. Chimpanzees probably discovered that same thing at some point because some actively seek it out to get hammered, which to me hilarious and fascinating. Sometimes discovery is just that, no experimentation is required. Vinegar could have been the result of some pre-agricultural hooman making wine who forgot about their batch.

Anonymous at Fri, 6 Sep 2024 12:19:34 UTC No. 16363694

>>16360914
professor leonard on youtube + textbook

try your best to understand the intuition behind the concepts, that will be more fruitful to your learning rather than just going through the motions(heh)

Anonymous at Fri, 6 Sep 2024 13:59:33 UTC No. 16363789

>>16360560
>I feel like there is some leap in logic
Yeah, I've been there too, but it all makes sense when you get a good grasp of the theory. Your results are correct, the quotient is trivial.

As for the suggestion from the other anon, remember that [math]\mathbb{R}[x][/math] is an euclidean ring, which means that for any [math]f, g \in \mathbb{R}[x][/math] there are some (unique) [math]q, r \in \mathbb{R}[x][/math] such that [math]f(x)=g(x)q(x)+r(x)[/math] with [math]r=0 \text{ or } deg(r) < deg(g)[/math]. That explains a lot of the structure of the quotients of [math]\mathbb{R}[x][/math].

Anonymous at Fri, 6 Sep 2024 16:57:46 UTC No. 16364032

so there is no point in speaking up during group work right? if you're consistently wrong people will not listen to you/you're ideas and since you don't have to prove anything to anyone except the teacher you only should focus on doing well on quizzes/exams correct?

Anonymous at Fri, 6 Sep 2024 17:47:39 UTC No. 16364104

>>16364032
>speaking up during group work
What does this mean? Just say what you think and if you're wrong then you learn something new.

Anonymous at Fri, 6 Sep 2024 17:54:44 UTC No. 16364113

>>16363789
Thanks. That euclidean ring thing makes this make a lot more sense.
Looking at it more I'm pretty sure for all polynomials [math]f\in\mathbb{R}[/math], [math]\langle f\rangle[/math] is contained in any ideal generated by a factor of [math]f[/math]. So any linear polynomial (or any unfactorable polynomial) [math]g[/math] would generate a maximal ideal, which makes [math]\mathbb{R}[x]/\langle g\rangle[/math] a field. Then any quotient of [math]\mathbb{R}[x]/\langle g\rangle[/math] must be isomorphic to [math]\mathbb{R}[x]/\langle g\rangle[/math] or [math]\{\varnothing\}[/math].
On top of this the zeroes of [math](\mathbb{R}[x]/\langle x-1\rangle)\langle\overline{x+1}\rangle[/math] were polynomials which could be written as [math]p(x)(x-1)-q(x)(x+1)[/math], which is every polynomial since [math]p(x)=-\frac{1}{2}p(x)(x-x-1-1)=-\frac{1}{2}p(x)(x-1)-(-\frac{1}{2}p(x))(x+1)[/math]
Man algebra is wack but also fun as hell.

Anonymous at Fri, 6 Sep 2024 18:09:09 UTC No. 16364127

>>16364032
From the perspective of "the smart guy" who would "always do all the work" in groups --

Why would you WANT to speak up in a group?

Anonymous at Fri, 6 Sep 2024 18:15:03 UTC No. 16364135

>>16364127
participation grade

Anonymous at Fri, 6 Sep 2024 18:50:29 UTC No. 16364172

>>16364104
Yeah I wish it was as simple as that but people require you to be right when you speak or else what's the point in listening to that individual?

Anonymous at Fri, 6 Sep 2024 22:49:37 UTC No. 16364695

Do particles without a magnetic field still exhibit the double-slit effect?

Anonymous at Fri, 6 Sep 2024 22:55:08 UTC No. 16364708

>>16364695
Yes. Electromagnetism has nothing to do with the result of the experiment.

Anonymous at Fri, 6 Sep 2024 22:59:34 UTC No. 16364715

>>16364708
I don't care what the theory says tho, I wanna know if it's been tested. Or do non-magnetic particles not exist?

Anonymous at Fri, 6 Sep 2024 23:01:00 UTC No. 16364716

>>16364715
you can do it with neutrons or photons. neither have an electric change.

Anonymous at Fri, 6 Sep 2024 23:04:22 UTC No. 16364720

>>16364716
I said magnetic, not electric.

Anonymous at Fri, 6 Sep 2024 23:05:47 UTC No. 16364723

>>16364720
NTA but any moving electric charge has a magnetic field

Anonymous at Fri, 6 Sep 2024 23:05:59 UTC No. 16364724

>>16364720
I don't think you know the difference.

Anonymous at Fri, 6 Sep 2024 23:09:38 UTC No. 16364729

>>16364724
Please keep your retarded opinions to yourself kthx

>>16364723
Neutrons are uncharged and have a magnetic field though

Anonymous at Fri, 6 Sep 2024 23:12:50 UTC No. 16364735

>>16364729
> Neutrons are uncharged and have a magnetic field though
Because of their internal structure (a composite of quarks). It's tiny btw and can almost always be ignored.

I'm curious why you would even think having a magnetic moment would affect the result of the double-slit experiment?

Anonymous at Fri, 6 Sep 2024 23:16:07 UTC No. 16364739

>>16364735
All I know about magnetic flux loops is they're unbreakable, unstoppable, and store some kind of momentum-like information (not sure if relevant). Seems pretty sus to me.

Anonymous at Fri, 6 Sep 2024 23:20:20 UTC No. 16364743

>>16364739
that reads like schizo babble and has no relevance at all.

Anonymous at Fri, 6 Sep 2024 23:20:56 UTC No. 16364745

>>16364729
Neutron doesn't have a charge but it kinda does
https://en.wikipedia.org/wiki/Neutron_electric_dipole_moment

Anonymous at Fri, 6 Sep 2024 23:25:51 UTC No. 16364753

>>16364745
>So far, no neutron EDM has been found.
Well I'm at least glad people are trying

Anonymous at Fri, 6 Sep 2024 23:28:53 UTC No. 16364759

Why did my ODE class (Hirsch and Smale 1e) cover Rational Canonical Form?

What are its benefits over JNF?

god ive been wondering this for weeks...

Is it just to demonstrate that a JNF matrix can be de-complexified?
It doesnt appear to have any computational benefit.

Anonymous at Fri, 6 Sep 2024 23:29:01 UTC No. 16364760

>>16364753
here's a tl;dr version
anyway a moving neutron definitely affects charge carrying particles and creates a weak electric field in the process

Anonymous at Sat, 7 Sep 2024 07:07:31 UTC No. 16365434

i just started learning biomechanics and have no idea what any of my professors lectures have to do with the assignments hes giving us. Is there like a basic resources page for symbols and formulas? the trig section is also beating me up aswell.