Anonymous at Sun, 16 Feb 2025 02:31:27 UTC No. 16587495

>>16587488

Anonymous at Sun, 16 Feb 2025 02:33:58 UTC No. 16587497

>>16587495
Nobody really gives a fuck about rigor anymore. Anything goes now honestly. The same kinda shit that happened to physics is now happening to mathematics.

Anonymous at Sun, 16 Feb 2025 03:03:24 UTC No. 16587525

>>16587488
>>16587497
Mathematical research goes in phases. Certain topics become popular while other become less popular.

Research in the axiomatic foundations of mathematics was tied to the formalization of mathematics and the discovery of many paradoxes as a result in the mid to late 1800s.

Computers and their applications/uses in various fields like machine learning, graphics, physical simulations, etc are now driving a lot of mathematics now and the logical foundations of math wasn never that popular to begin with.

Mathematics as a field is fine.

Anonymous at Sun, 16 Feb 2025 04:03:23 UTC No. 16587561

>>16587488
rip my nigga Euclid - I love you and I love all Euclidian mathematicians. and all the mathematicians who worked with Euclid to get the propositions constructed properly... hundreds of men, and all of them geniuses.

you are my goats and we still remember you to this day and we study your texts. you are my super goat Mr. Euclid <3

rip in heaven THE GOAT EUCLID <3

Anonymous at Sun, 16 Feb 2025 05:24:07 UTC No. 16587600

ZFC? Isn't that the system ancient people used before type theory?

Anonymous at Sun, 16 Feb 2025 13:51:34 UTC No. 16587884

>>16587488
>ZFC

It's a novelty because it can't even prove the most basic intuitive things about sets. Only has notice because of historical interest.

Anonymous at Sun, 16 Feb 2025 15:12:35 UTC No. 16587960

>>16587488
You are mistaking foundations of set theory with foundations of a subject like, say, differential equations. I highly doubt that an algebraic geometer doesn't know the group axioms, or a differential geometer the formal definition of compactness.

Set theory foundations is, and should be, orthogonal to other subject. Tell me, when is it ever necessary to use the fact that 0 is the empty set? In fact, in ZFG, you should know that it might even be false, since constructions are only unique up to set isomorphism.

As I see it, foundations was born to justify what other mathematicans were doing. ZFC should (almost, see the Grothendieck universe axiom) never matter to a normal mathematician. What should matter to them is that some other mathematicians have created some foundations from which they can work. In fact, since ZFC is not the only foundation, simply learning ZFC could make them biased (I personally dislike ZFC and prefer ETCS.)

People are very much still working on foundations. ZFC not much, there are more interesting models. Type theory is alive and well, homotopy type theory is still new but active and in some years we migth see very interesting developments. And there is a community of mathematicians working with Lean formally proving many different theorems from the very foundations of mathematics. So to answer your question: not at all.

Anonymous at Sun, 16 Feb 2025 15:15:41 UTC No. 16587964

>>16587960
(me) This paper talks somewhat about this topic: https://arxiv.org/pdf/1212.6543

Anonymous at Sun, 16 Feb 2025 16:14:03 UTC No. 16588015

>>16587960
You are euclid illiterate aren't you

Anonymous at Sun, 16 Feb 2025 17:11:19 UTC No. 16588080

>>16587960
Set Theory is the foundations for all of mathematics.

Anonymous at Sun, 16 Feb 2025 17:16:41 UTC No. 16588084

>>16587488
Straight-edges and compasses are fine for sandbox play, but I have access to the Internet.

Anonymous at Sun, 16 Feb 2025 17:40:30 UTC No. 16588120

>>16588084
I have access to the internet

Anonymous at Sun, 16 Feb 2025 17:46:38 UTC No. 16588133

>>16588120
Totally devoid of creativity or originality. Pathetic.

Anonymous at Sun, 16 Feb 2025 23:37:33 UTC No. 16588568

>>16587561
why you forget my negga archimedes? :(

Anonymous at Mon, 17 Feb 2025 00:24:14 UTC No. 16588594

>>16588133

Anonymous at Mon, 17 Feb 2025 00:28:13 UTC No. 16588598

>>16587488
embrace monke'.

Anonymous at Mon, 17 Feb 2025 00:45:28 UTC No. 16588611

>>16588598
Your post is old and only the newest post matters, no point in reading the thread only the new post matters, the original post be damned and the subsequent posts as well, only the new post matters

Anonymous at Mon, 17 Feb 2025 01:01:10 UTC No. 16588620

>>16588568
Ptolemy as well my negro

Anonymous at Mon, 17 Feb 2025 01:39:50 UTC No. 16588643

>>16588620
does my nigra pythagoras count? =3

Anonymous at Mon, 17 Feb 2025 01:53:44 UTC No. 16588647

>>16587495
>>16587488
>a point is that which has no part
Wow, so constructive! That certainly isn’t a mumbo-jumbo statement. What is a part? Is this “part” ever mentioned again in Euclidean geometry?

Anonymous at Mon, 17 Feb 2025 02:31:37 UTC No. 16588671

>>16587488
>The average math student
Ok, then show me the average math major curriculum or anything that supports that
>>16587960
>>16587964
>Tom Leinster
These are his notes
https://www.maths.ed.ac.uk/~tl/ast/ast.pdf
>I’m teaching Edinburgh’s undergraduate Axiomatic Set Theory course, and the axioms we’re using are Lawvere’s Elementary Theory of the Category of Sets — with the twist that everything’s going to be done directly in terms of sets and functions, without invoking categories. That is, I’ll neither assume nor teach the general notion of category.
>I thought I’d share my notes so far.

Anonymous at Mon, 17 Feb 2025 02:35:41 UTC No. 16588672

>>16588671
>I’ll sneakily teach them category theory
gigabased. Every “naive” introduction to set theory already teaches it in the categorical sense. Consider, for example, how functions between sets are commonly represented as arrows connecting dots. This is way more intuitive to your average normalfags than the set theoretic construction with Cartesian products and quantifiers.

Anonymous at Mon, 17 Feb 2025 02:48:34 UTC No. 16588684

>>16587964
The category theory inspired stuff is making this needlessly unnatural.
>elements of a set are functions from a single-element set (so that composition can be the basic concept instead of application)
>to use a member of what ought to be the set of functions from A to B, you need to use an evaluation function

Anonymous at Mon, 17 Feb 2025 02:59:38 UTC No. 16588695

>>16588080
Not the only foundation.

Anonymous at Mon, 17 Feb 2025 03:05:19 UTC No. 16588700

>>16588647
Saying it has no part stops the infinite regression of turtles all the way down and creates a foundation to build upon such as any 2 points can be connected with a line

"what is without parts is a point for
my purposes and a principle for me; and the simplest object
is none other than this.” In such fashion must we understand
the statement of our geometer.

Anonymous at Mon, 17 Feb 2025 03:27:53 UTC No. 16588719

>>16588700
Sure, sure. Define part doe. Because so far that statement is semantically equivalent to
>a gurble is that which has no twirple

Anonymous at Mon, 17 Feb 2025 03:28:19 UTC No. 16588720

OP, there's more to math than geometry and math people who are really hardcore at geometry get jobs making 3d imaging machines. You can get such a job too.

Anonymous at Mon, 17 Feb 2025 03:36:10 UTC No. 16588725

>>16588719
Go back to reddi.t with your gurble twirple

Anonymous at Mon, 17 Feb 2025 03:41:26 UTC No. 16588730

>>16588720
Engineers and physicists are NOT mathematicians. I will never get a job, you can't make me

Anonymous at Mon, 17 Feb 2025 03:44:00 UTC No. 16588733

>>16588725
Typical. Notice that ZFC set theory doesn’t make these synthetic statements. There are only elements, which are themselves sets. So no need to speak of “X of Y” because there’s only X.

Anonymous at Mon, 17 Feb 2025 03:46:24 UTC No. 16588739

>>16588720
There's more to live than making 3d imaging machines, people that are hardcore at life do rock climbing and you can just climb shit without a job, you can get such a life too

Anonymous at Mon, 17 Feb 2025 03:52:51 UTC No. 16588744

>>16588733
Zfc set theory Pythagoras theorem

Anonymous at Mon, 17 Feb 2025 04:00:29 UTC No. 16588749

>>16588744
Once again, I fail to see how statements like “for all pairs of points there exists a line crossing this pair” are constructive. It’s purely an existence statement, no different from constructions in set theory. Just because you draw or don’t draw the line doesn’t make it constructive. The axioms imply the line is always there without any logical construction involved.

Anonymous at Mon, 17 Feb 2025 04:14:25 UTC No. 16588756

>>16588749
Zfc can't into Pythagoras

Anonymous at Mon, 17 Feb 2025 04:28:26 UTC No. 16588767

>>16588756
Ehmm it can? Just watch.
1. Construct the empty set from the axiom of infinity
2. Construct the power set of the empty set by the axiom of the power set. Call it 1 for simplicity.
3. Construct the free group F(1), call this group integers
4. Endow integers with ring structure
5. Construct the polynomial ring in one variable with integer coefficients
6. Extend this ring to the field of rationals by taking successive quotients of prime numbers
7. Dedekind complete the set of rationals to obtain the reals
8. Algebraically complete the set of reals by first constructing the polynomial ring R[x] and then taking the quotient R[x]/(x^2+1). Call this quotient the complex numbers.
9. The complex numbers also happen to be vector spaces, since all rings are free Z-modules.
10. Endow this vector spaces with the unique quadratic norm (unique in the sense of respecting its algebraic propeties)
11. Consider a complex number c=a+bi. By the definition of its unique quadratic norm.

a^2 + b^2 = c^2

QED

Skill issue

Anonymous at Mon, 17 Feb 2025 04:35:14 UTC No. 16588773

>>16588749
It's "To draw a straight line from any point to any point." It's not an existence statement. It's an action you can perform.

Anonymous at Mon, 17 Feb 2025 04:38:22 UTC No. 16588780

>>16588773
And “for all x in X there exists a unique y in Y” is also an action you can perform. It’s called constructing a function. It gives you an instruction on how to do so. Just like how Euclid instructs you to draw a line between two points. Euclid’s axioms claim that this is possible for any two points and such a line is unique. Literally no different from a function. “For any two points there exists a unique line between them” The points are arguments of a function and the line is the output. You can construct or not, it’s your choice.

Anonymous at Mon, 17 Feb 2025 04:43:17 UTC No. 16588786

>>16588780
Yeah, you can call it a function. But there are functions you can compute and other functions where you can prove for every x there's a unique y, but you can't actually calculate what y is given x. That's the difference between constructive and not constructive. In Euclid's Elements, the constructions are not merely existence proofs. They show how to create the required geometric figure with a straightedge and compass.

Anonymous at Mon, 17 Feb 2025 04:46:40 UTC No. 16588790

>>16588786
What’s “calculating a line” supposed to mean?
>They show how to create the required geometric figure with a straightedge and compass.
What’s “straightedge and compass”? Some other mumbo jumbo that Euclidean geometry needs to make synthetic judgments about. It certainly has nothing to do with real straightedges and compasses, because the former doesn’t extend to infinity and the latter can’t make perfect circles, it has physical limitations due to things like coarseness of the paper, fineness of lead, etc etc.

Anonymous at Mon, 17 Feb 2025 04:55:20 UTC No. 16588798

>>16588767
Dungeons and dragons make up stuff ass mathematics

Anonymous at Mon, 17 Feb 2025 05:02:00 UTC No. 16588803

>>16588798
As I said, skill issue. Git gud. Behind all this jargon is a single object, the empty set. Everything else is essentially a set containing sets, containing sets containing the empty set, all constructed using rules of predicate logic. At its core, I’ve proven the Pythagorean theorem using a single object.

Whereas euclidlets need three complete independent and ill-defined objects called a point, a line, and a circle, which are only related to each other axiomatically (a priori synthetically in Kantian terms). And Euclid needs some deus ex machina for each to justify its existence, a “part”, a “straightedge”, and a “compass”. See >>16588790. None of this is in any way related via predicate logic. Literally shit he pulled out of his ass based on “intuition”.

Anonymous at Mon, 17 Feb 2025 05:04:51 UTC No. 16588804

>>16588803
You didn't write out a proof, you outlined one in prose with about 99.9% of the details missing. If you actually wrote out formal proofs even as a hobby you wouldn't be ass-licking ZFC.

Anonymous at Mon, 17 Feb 2025 05:06:29 UTC No. 16588805

>>16588804
Of course I didn’t write out a formal proof. I would probably hit bump limit if I did. Everything I said is undergraduate math curriculum.
Git
gud

Anonymous at Mon, 17 Feb 2025 05:15:11 UTC No. 16588812

>>16588805
Look at this proof for Pythagoras, write your proof out and post it, you so have access to the internet

Anonymous at Mon, 17 Feb 2025 05:15:28 UTC No. 16588813

>>16588805
Most undergrads don't write out formal proofs either. Homework assignments are normally written in prose, albeit with all the necessary details for a code monkey to turn it into a formal proof. I think there are a few professors who have students write out formal proofs as an undergrad research project, but they're not going to be using ZFC for that. Most likely Lean.

Anonymous at Mon, 17 Feb 2025 05:19:17 UTC No. 16588818

>>16588812
Good. Now prove that every polynomial curve of degree n admits maxima and minima using a straightedge and compass. I dare you. The beauty of set theory is that it allows you to work in a single framework for all mathematics. And it does that with a single object called a set. Not three objects. One.

Euclid apparently doesn’t believe curves exist, because my hand isn’t a straightedge. What’s the utility in this? I can use powerful tools of algebra and topology to study non-linear geometry, while you draw “straight” lines on sand and plug your ears when people tell you that’s not all of geometry.

Anonymous at Mon, 17 Feb 2025 05:21:17 UTC No. 16588820

>>16588813
Expecting mathematicians to write out proofs in first order language is like expecting programmers to write everything in machine code. They technically can, but why would they? We, humans, have this powerful ability called abstraction.

Anonymous at Mon, 17 Feb 2025 05:34:49 UTC No. 16588828

>>16588818
You still can't do Pythagoras, send a link to a proof and I bet it's as contrived as the trigonometric proof of those black girls

Anonymous at Mon, 17 Feb 2025 05:45:20 UTC No. 16588836

>>16588828
I just outlined the proof. Your failure to understand what I said is your problem. I refer you to basic texts like Artin’s Algebra.

If your whole argument boils down to “muh proof too long”, then I can do better than you. I simply postulate the Pythagorean theorem as an axiom, independently of any other axiom. Bam, done. Is this any useful? No, of course not. Why? Because it has a limited scope.

In the same way, Euclidean geometry has a very limited scope. It ignores curves, certainly something that is “intuitive” and “constructive” according to retards who inhabit these threads. But ZFC has a much broader scope. As a result, there are more deductive steps required to go from the axioms to a particular statement. Does that somehow make it le bad? Quite the opposite, because the number of statements it can prove vastly mogs those of Euclidean geometry, allowing one to understand the intricate connections between these statements. Neither algebraic nor differential geometry can be derived from Euclidean geometry. But they can be derived from ZFC. So keep coping with your “le shorter proofs” brainlet arguments.

Anonymous at Mon, 17 Feb 2025 05:46:56 UTC No. 16588838

>>16587525
AI "Programmers" are the shittiest mathematicians I've ever had the displeasure of encountering.

Anonymous at Mon, 17 Feb 2025 06:01:03 UTC No. 16588847

>>16588836
There is no shorter proof argument going on nor is there a geometry only argument going on, these are just some shit you made up like schizo projections to attack

Anonymous at Mon, 17 Feb 2025 06:07:35 UTC No. 16588852

>>16588818
Computers only know straight lines.
>>16588828
I got bored one day and figured out this version.

Anonymous at Mon, 17 Feb 2025 06:09:53 UTC No. 16588853

>>16588847
You sound incoherent and your argument is unconvincing.

Anonymous at Mon, 17 Feb 2025 06:17:53 UTC No. 16588858

>>16588847
>these are just some shit you made up
Oh, I didn’t. Much smarter people than me came up with all this. I have already mentioned Artin. Algebra is a fascinating subject.
>>16588852
Nigga’s never heard of Bezier curves.

Anonymous at Mon, 17 Feb 2025 06:24:45 UTC No. 16588866

>>16588858
You brought in an outside variables bullshit and decided to rant about it like people here were taking about proof length and denial of any mathematics beyond euclids straight line.... that's crazy dude

Anonymous at Mon, 17 Feb 2025 06:32:37 UTC No. 16588874

>>16588866
>outside variables
I have no idea what that means. No “outside” definitions were used. Free groups, modules, quadratic norms, etc are all sets.
>rant about it like people here were taking about proof length and denial of any mathematics beyond euclids straight line
The original post I replied to claimed the Pythagorean theorem is outside the scope of ZFC. I provided an outline of how to prove the Pythagorean theorem from the ground up starting with the empty set, its power set, and various other jargon-heavy things that are sets in their essence and are obtained through power sets, set unions and the axiom of schema of specification. So I delivered.

Then the nigger started coping by saying it’s not a real proof because uhhhhhhhh it just isn’t ok? I didn’t write the whole thing down in first order language so it’s obvious false. Ok? Then he showed some bullshit scribbles going “huh, I just proved the Pythagorean theorem”. Ok? I did too.
tl;dr you’re all dumb niggers who short-circuit when exposed to math beyond high school level stuff

Anonymous at Mon, 17 Feb 2025 06:46:27 UTC No. 16588887

>>16588874
Why did op say "The only people still discussing things like ZFC are philosophers"

Anonymous at Mon, 17 Feb 2025 06:47:17 UTC No. 16588888

>>16588887
I wasn’t responding to OP. If you can’t follow the chain of responses, then here >>16588756.

Anonymous at Mon, 17 Feb 2025 06:53:00 UTC No. 16588890

>>16588888
Op is the original post that prompted all other posts in the chain

Anonymous at Mon, 17 Feb 2025 06:54:25 UTC No. 16588892

We are going to take a critical look at zfc

Anonymous at Mon, 17 Feb 2025 06:55:10 UTC No. 16588893

>>16588890
No way! So we should all strictly stick to OP and never veer away? Fuck, man, you just revealed some deep truth right here. Proved Zorn’s Lemma, basically.

Anonymous at Mon, 17 Feb 2025 06:59:01 UTC No. 16588894

>>16588893
OK, thoughts on this image?

Anonymous at Mon, 17 Feb 2025 07:00:57 UTC No. 16588895

Thoughts on proof by contradiction?

Anonymous at Mon, 17 Feb 2025 07:01:27 UTC No. 16588896

>>16588894
I miss Seinfeld posting on /tv/ desu. It’s such a shit board these days.

Anonymous at Mon, 17 Feb 2025 07:16:30 UTC No. 16588899

>>16588895
~P is by definition P -> False, so it makes sense to prove it that way.

Anonymous at Mon, 17 Feb 2025 07:36:41 UTC No. 16588906

>>16587497
>Anything goes now honestly.
Anything has gone ever since they decided to allow the origin number to be its own opposite to manifest an infinite explosion of multiples.

Anonymous at Mon, 17 Feb 2025 07:50:00 UTC No. 16588914

>IT has been customary when Euclid, considered as a text-book, is attacked for his verbosity or his obscurity or his pedantry, to defend him on the ground that his logical excellence is transcendent, and affords an invaluable training to the youthful powers of reasoning. This claim, however, vanishes on a close inspection. His definitions do not always define, his axioms are not always indemonstrable, his demonstrations require many axioms of which he is quite unconscious. A valid proof retains its demonstrative force when no figure is drawn, but very many of Euclid’s earlier proofs fail before this test.
>The first proposition assumes that the circles used in the construction intersect – an assumption not noticed by Euclid because of the dangerous habit of using a figure. We require as a lemma, before the construction can be known to succeed, the following: If A and B be any two given points, there is at least one point C whose distances from A and B are both equal to AB. This lemma may be derived from an axiom of continuity. The fact that in elliptic space it is not always possible to construct an equilateral triangle on a given base, shows also that Euclid has assumed the straight line to be not a closed curve – an assumption which certainly is not made explicit. When these facts are taken account of, it will be found that the first proposition has a rather long proof, and presupposes the fourth. We require the axiom: on any straight line there is at least one point whose distance from a given point on or off the line exceeds a given distance.

Anonymous at Mon, 17 Feb 2025 07:51:01 UTC No. 16588915

>The fourth proposition is a tissue of nonsense. Superposition is a logically worthless device; for if our triangles are spatial, not material, there is a logical contradiction in the notion of moving them, while if they are material, they cannot be perfectly rigid, and when superposed they are certain to be slightly deformed from the shape they had before. What is presupposed, if anything analogous to Euclid’s proof is to be retained, is the following very complicated axiom: Given a triangle ABC and a straight line DE, there are two triangles, one on either side of DE, having their vertices at D, and one side along DE, and equal in all respects to the triangle ABC. (This axiom presupposes the definition of the two sides of a line, for which see below.) When the existence of a triangle thus equal in all respects to ABC is assured, we can prove that the triangle considered in the fourth proposition is this triangle.
>The sixth proposition requires an axiom which may be stated as follows: If OAA′, OBB′, OCC′ be three lines in a plane, meeting two transversals in A, B, C, A′, B′, C′ respectively; and if O be not between A and A′, nor B and B′, nor C and C′, or be between in all three cases; then, if B be between A and C, B′ is between A′ and C′. This axiom is the basis of the measurement of angles by distances, and is required for proving that if D be on AB, and BD be less than BA, the triangle DBC is less than the triangle ABC.

Anonymous at Mon, 17 Feb 2025 07:52:01 UTC No. 16588917

>The seventh proposition is so thoroughly fallacious that Euclid would have done better not to attempt a proof. In the first place, it uses an undefined term in the enunciation, namely, on the same side. The definition requires an axiom, and may be set forth as follows: Given a line AB and a point C, with regard to any point D in the plane ABC, three cases may arise; (1) the straight line CD does not meet AB; (2) CD meets AB, produced if necessary, in a point not between C and D; (3) CD meets AB in a point between C and D. In cases (1) and (2), C and D are said to be on the same side of AB; in case (3), on opposite sides. The above very complicated axiom is better replaced by the following two: (1) Given three points A, B, C, a point D between B and C, and a point G between A and D, BG produced meets AC in a point between A and C; (2) A, B, C, D being as before, and E being between A and C, AD and BE meet in a point between A and D and also between B and E.1 (The definition of between is long, and I omit it here for want of space.) The proof of I.7 further assumes that if C and D be on the same side of AB, then if CB is between CA and CD, DA is between DC and DB; while if CB is between CD and AC produced, then AD produced is between DC and DB. This is a very complicated assumption, of which Euclid is to all appearance completely ignorant. The assumption may be stated more simply as follows: Of three lines in a plane starting from a point, either there is one which is between the other two, or else any one of them produced is between the other two. But in this statement, the meaning of between has to be very carefully defined.

Anonymous at Mon, 17 Feb 2025 07:53:02 UTC No. 16588918

>I.8 involves the same fallacy as I.4, and requires the same axiom as to the existence of congruent triangles in different places. In the following propositions, we require the equality of all right angles, which is not a true axiom, since it is demonstrable.2 I.12 involves the assumption that a circle meets a line in two points or in none, which has not been in any way demonstrated. Its demonstration requires an axiom of continuity, by the help of which the circle can be dispensed with as an independent figure.
>I.16 is false in elliptic space, although Euclid does not explicitly employ any assumption which fails for that space. Implicitly, he uses the following: If ABC be a triangle, and E the middle point of AC; and if BE be produced to F so that BE=EF, then CF is between CA and BC produced. In spaces where the straight line is not a closed series, this follows from the axioms mentioned in connection with I.6 and I.7. No other points of interest, except that I.26 involves the same fallacy as I.4 and I.8, arise until we come to parallels; and the treatment of parallels in Euclid is, so far as I know, wholly free from logical defects.
>Many more general criticisms might be passed on Euclid’s methods, and on his conception of Geometry; but the above definite fallacies seem sufficient to show that the value of his work as a masterpiece of logic has been very grossly exaggerated.
B. RUSSELL

Anonymous at Mon, 17 Feb 2025 07:55:27 UTC No. 16588920

>>16588914
>A valid proof retains its demonstrative force when no figure is drawn, but very many of Euclid’s earlier proofs fail before this test.
Garbage criterion, garbage argument.

Anonymous at Mon, 17 Feb 2025 07:59:12 UTC No. 16588923

>>16588920
Why do you need scribbles to understand something? Are you a child?

Anonymous at Mon, 17 Feb 2025 08:00:18 UTC No. 16588925

>>16588923
wordcel

Anonymous at Mon, 17 Feb 2025 08:02:38 UTC No. 16588928

>>16588925
Picturecel.
>Lee Kuan Yew was the first President of Singapore
>Lee Kuan Yew was Chinese
>Therefore the first President of Singapore was Chinese
Draw me a diagram for this simple syllogism. Do you fail to capture information from it because I didn't doodle it to you?

Anonymous at Mon, 17 Feb 2025 08:03:54 UTC No. 16588930

>>16588928
I can use both words and pictures where appropriate.

Anonymous at Mon, 17 Feb 2025 08:07:02 UTC No. 16588933

>>16588930
And Russell pointed out how using pictures naively produces holes in arguments that require additional assumptions. Something that doesn't happen in first-order logic. Consider the graph in picrel. Did I draw a continuous function?

Anonymous at Mon, 17 Feb 2025 08:11:33 UTC No. 16588940

>>16588933
>using pictures naively
Then don't use them naively.
>Consider the graph in picrel. Did I draw a continuous function?
That looks like Desmos, so no way to tell. A proper geometric diagram should have the same topology as what it's intended to represent.

Anonymous at Mon, 17 Feb 2025 08:15:57 UTC No. 16588946

BTW stuff like this and not Russell's many dense pages of autism to prove 1+1 is what has de facto replaced Euclid in modern high schools. I hope you're happy.

Anonymous at Mon, 17 Feb 2025 08:19:17 UTC No. 16588949

>>16588940
>A proper geometric diagram should have the same topology as what it's intended to represent.
And how do you demonstrate this topology? By labeling holes with circles? That sounds like WORDS. And it certainly doesn't seem intuitive at all. Sounds like something someone needed to do because he looked at WORDS first and realized it needs to be there. Someone looking purely at the shape of this function cannot tell whether it's continuous or not.

Btw this was a trick question. This could be the graph of either
[eqn]f(x)=\frac{\sin{x}}{x}[/eqn]
or
[eqn]g(x)=\begin{cases}\frac{\sin{x}}{x}, x\not=0 \\ 1, x=0\end{cases}[/eqn]
The graph itself, without any WORDS or cope substitute for words like "we use a circle to indicate a feature, but there's no actual circle there", looks exactly the same. But the first function isn't even defined at x=0, so it's not continuous. The second function is perfectly fine and continuous. Did muh scribbles help?

Anonymous at Mon, 17 Feb 2025 08:58:34 UTC No. 16588985

>>16588946
and this

Anonymous at Mon, 17 Feb 2025 09:05:38 UTC No. 16588995

>>16588946
>>16588985
American math is grim

Anonymous at Mon, 17 Feb 2025 09:12:50 UTC No. 16589005

>>16588080
Incorrect. It's just a way to unify the different axiomatic systems of different branches into one.

Anonymous at Mon, 17 Feb 2025 13:09:39 UTC No. 16589211

>>16588719
It means a point has 0 dimensions, 0 sub-point, 0 external metrics, 0 length, 0 width, 0 height, ..., 0 of anything the higher level elements built upon points will eventually necessitate.

Anonymous at Tue, 18 Feb 2025 00:33:13 UTC No. 16589721

>>16588643
Yes, any respect for my nigguh hipparchus

Anonymous at Tue, 18 Feb 2025 04:43:54 UTC No. 16589844

>>16588080
big if tru

Anonymous at Tue, 18 Feb 2025 14:34:35 UTC No. 16590216

>>16589211
That’s like, just your opinion man and this is nowhere stated in the Elements. You are retroactively applying modern vector algebra notions to the Greeks who didn’t even have the Cartesian coordinates.

Anonymous at Tue, 18 Feb 2025 15:04:46 UTC No. 16590245

>>16587488
Set theory is a retarded subject with no connection to reality.

Anonymous at Tue, 18 Feb 2025 15:19:09 UTC No. 16590264

>>16590245
as if any math at all has any connection to reality

Anonymous at Tue, 18 Feb 2025 15:22:02 UTC No. 16590268

>>16590264
Are you just pretending to be stupid? I cannot believe anyone can actually be this stupid while using the internet.

Anonymous at Tue, 18 Feb 2025 17:05:56 UTC No. 16590415

>>16590268
oh, i see you where meaning to respond to >>16590245, no need to thank me for clarifying

Anonymous at Tue, 18 Feb 2025 17:11:51 UTC No. 16590424

>>16590415
You "saw" that? Or did you just hallucinate it? Like the sets hallucinated by set theorists

Anonymous at Tue, 18 Feb 2025 19:29:31 UTC No. 16590567

>>16588858
>Bezier curves
You clearly have no idea how computers construct those.
Hint (A whole bunch of tiny straight lines)

Anonymous at Tue, 18 Feb 2025 19:32:37 UTC No. 16590574

>>16590245
Funny thing
Components of set theory is taught to grade schoolers and highschoolers but they never call it set theory even though it is part of all public school math curriculum in the US.

Open up any geometry book and behold the regular use of set theory (although never defined or explained).

Anonymous at Tue, 18 Feb 2025 19:57:30 UTC No. 16590595

>>16590574
Open up any geometry book and behold it takes part in the geometry of Euclid (although never defined or explained)

Anonymous at Tue, 18 Feb 2025 20:21:51 UTC No. 16590638

>>16590268
Name one thing in reality that is math. Point me to number one sitting out there in the universe.

Anonymous at Tue, 18 Feb 2025 20:36:21 UTC No. 16590653

>>16590638
Numbers are an emergent description which arises from the quanta of quantum mechanics. It's a valid approximate concept for macroscopic objects

Anonymous at Tue, 18 Feb 2025 20:38:56 UTC No. 16590656

>>16590653
>emergent description
And names are an emergent description of people. Point me to the word "Jason" out there in reality.

Anonymous at Tue, 18 Feb 2025 20:41:38 UTC No. 16590658

>>16590656
"Jason" is there on my computer screen right now.

Anonymous at Tue, 18 Feb 2025 20:45:24 UTC No. 16590663

>>16590638
You said number 1 then said universe and I don't think you understand the relationship between 1 and uni

Anonymous at Tue, 18 Feb 2025 20:53:07 UTC No. 16590676

>>16590658
That's just a bunch of atoms making up an LED. You abstract them away as letters.
>>16590663
based schizo

Anonymous at Tue, 18 Feb 2025 20:55:15 UTC No. 16590677

>>16590676
Sorry, I don't believe in these mystical "abstractions" that you seem to believe in. There is nothing more to Jason than "Jason"

Anonymous at Tue, 18 Feb 2025 20:59:16 UTC No. 16590681

>>16590677
So you really can't understand the basic deduction that our brains reconstruct a bunch of light signals received by our eyes and then your brain makes the correlation between a bunch of pixels and the word "Jason" in your head? That's just sad, man. You can write the name in chalk, you can pronounce it aloud, you can write it out in the sky with drones. All of these are different physical phenomena, yet the name Jason is still the same. You capisce?

Anonymous at Tue, 18 Feb 2025 21:02:35 UTC No. 16590686

>>16590681
Oooh monkey's having a melty because other monkey doesn't believe in monkey cult of abstractionism made up by big dumb ancient greek monkey. Wanna banana?

Anonymous at Tue, 18 Feb 2025 21:03:25 UTC No. 16590687

>>16590686
As I said, sad. Nigger IQ retard can't comprehend abstraction and basic epistemology.

Anonymous at Tue, 18 Feb 2025 21:06:44 UTC No. 16590689

>>16590687
Oooh monkey screeching philosophy department words like epistemology to scare away other monky

Anonymous at Tue, 18 Feb 2025 21:51:12 UTC No. 16590760

>>16590689
Very productive conversation. Thank you, anon.

Anonymous at Tue, 18 Feb 2025 21:54:29 UTC No. 16590763

>>16587600
I look like this and say this

Anonymous at Thu, 20 Feb 2025 05:26:45 UTC No. 16592183

>>16590595
There's a difference between not giving credit to a creator of the maths (Euclid) and not defining the math at all but still using it (set theory).

Anonymous at Thu, 20 Feb 2025 05:28:48 UTC No. 16592185

>>16590689
>>16590686
I don't even care if you're right or wrong, you're clearly losing your shit.

Anonymous at Thu, 20 Feb 2025 06:00:15 UTC No. 16592212

>>16592185
Monkey seems to be hallucinating. Try smashing head on hard rock

Anonymous at Thu, 20 Feb 2025 06:30:03 UTC No. 16592223

>>16592212
Did you have to say hard Rock? Did you think his nearest rock could be a soft rock

🗑️ Anonymous at Thu, 20 Feb 2025 06:34:15 UTC No. 16592227

Jesus Christ died for our sins and rose from the dead to give us the free gift of eternal life in heaven and promised to heal your body. Just Look up and ask Him.

Anonymous at Thu, 20 Feb 2025 08:17:34 UTC No. 16592295

>>16587488
>The average math student never really learns about the axiomatic foundations of math.
Why learn A=A when you can learn identity politics in math class? :^)

Anonymous at Thu, 20 Feb 2025 08:37:57 UTC No. 16592305

>>16592295
Why did your parents lobotomize you as a child?

Anonymous at Sat, 22 Feb 2025 15:46:17 UTC No. 16596439

>>16592295
big if true

Anonymous at Sun, 23 Feb 2025 00:02:46 UTC No. 16596919

>>16587600
silly anime girl, you can't make the problem go away by just making up a new rule that says you're allowed to never look at the problem

Anonymous at Sun, 23 Feb 2025 16:19:59 UTC No. 16597395

>>16588838
Of course. AI at the moment is like the steam engine craze of the 1800s: people just trying shit and seeing if it sticks. Time will tell if there is a more cohesive mathematical theory surrounding the field, but as it stands, a lot of AI industry and academic researchers are just overhyped codemonkeys.

Anonymous at Sun, 23 Feb 2025 16:56:48 UTC No. 16597416

>>16587960
>And there is a community of mathematicians working with Lean formally
damn I never should of dropped out, I would have been doing the same thing anyways