Anonymous at Tue, 4 Jun 2024 09:32:32 UTC No. 16209472

>>16209467

factorial is how many ways a set can be arranged

0 elements can be arranged in one way (0)

2! elements can be arranged in 2 ways (1, 2), (2, 1)

3! elements can be arranged in 6 ways (1, 2, 3), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1), (1, 3, 2)

and so on, and so forth

Anonymous at Tue, 4 Jun 2024 09:35:05 UTC No. 16209474

>>16209472
fascinating pattern, no one had ever brought that to my attention, thanks!

Anonymous at Tue, 4 Jun 2024 09:39:58 UTC No. 16209481

>>16209467
>Is this science?
it is if someone took that mathematical tool, made an empirically testable prediction with it, and went out in the natural world to verify it, independently of it it was true or not. Negative results are science as well, since they nullify ideas which aren't true, and we move on to the next idea, etc.

>We don't care about truth
That's where theoretical mathematics blurs with philosophy, and that's beyond the scope of science. Mathematics is the mind-play that emerges from what we see in nature, as in "one apple + another apple = two apples, I wonder what happens if I keep adding apples forever...", science is the testing of the ideas that emerge out of that mind-play, as I explained above.

Anonymous at Tue, 4 Jun 2024 10:14:21 UTC No. 16209503

>>16209467
It is mathematics, and besides it has a very natural combinatorial interpretation and it is the only sensible base case for a recursive definition of factorials for all natural numbers.

Anonymous at Tue, 4 Jun 2024 11:07:24 UTC No. 16209555

>>16209467
>Is this science?
No, it's mathematics. Math isn't science. Math is *correct.*
> We don't care about truth but whether something is useful?
The only truth is self-consistency. If we can define something in a way that is useful, or intuitive, or natural, or subjectively elegant -- all well and good, so long as our assumptions are known and set in stone and the consequences are self-consistent.
Math doesn't exist to represent the universe. Scientists *use* math to model the universe, but that's ancillary. If something "doesn't make sense," good! Your brain didn't evolve to do math, any more than it evolved to listen to the Beatles or crash cars into walls. Keep reading math and it'll "make more sense," as your brain gets used to the structures that've been built up and can, in turn, understand larger and more complicated structures built on these.
Keep it up for ~8-10 years and you can get yourself a PhD; enormous luck and another 4-8 years in postdocs and you might just publish something that more than your advisor will ever read. You're not a one in a million, of course, so you'll probably never contribute more than a paper or two that has any *meaningful* impact, even if you throw away your life and any other hopes or dreams. But in doing research you'll have touched something that nobody else, not one other living human, has ever thought of before, and added it to the canon forever. Maybe that's enough.

Anonymous at Tue, 4 Jun 2024 12:25:31 UTC No. 16209657

>>16209467
4!=5!/5
3!=4!/4
2!=3!/3
1!=2!/2
0!=1!/1

Anonymous at Tue, 4 Jun 2024 13:10:09 UTC No. 16209703

look at the file name. It's explanatory

Anonymous at Tue, 4 Jun 2024 13:26:14 UTC No. 16209726

>>16209467
combinatorics empty product, meta-fool

Anonymous at Tue, 4 Jun 2024 13:26:26 UTC No. 16209727

>>16209472
I hate to say it but this is true
an empty set and singleton set are combinatorially the same.
This is why the gamma function is WAY better
See >>16209703
Plus it ties with the laplace transform plus it's continuous at 0!

Anonymous at Tue, 4 Jun 2024 13:28:15 UTC No. 16209733

>>16209726
ok, after seeing that you got it, i apologize for calling you a fool

Anonymous at Tue, 4 Jun 2024 13:28:47 UTC No. 16209735

>>16209555
>No, it's mathematics. Math isn't science. Math is *correct.*

Anonymous at Tue, 4 Jun 2024 13:46:22 UTC No. 16209758

I always thought a zero was a one.

Nothing is a something.

Think about it.

Anonymous at Tue, 4 Jun 2024 13:46:27 UTC No. 16209759

>>16209657
-1!=0!/0 ?

Anonymous at Tue, 4 Jun 2024 13:52:05 UTC No. 16209772

>>16209727
>an empty set and singleton set are combinatorially the same.
Except, for example, in the most fundamental of all combinatorial properties: the empty set has no elements while a singleton has one.

>This is why the gamma function is WAY better
What do you even mean by this?

Anonymous at Tue, 4 Jun 2024 14:17:23 UTC No. 16209805

>0!=1!
>Remove the ! on both sides
>0=1
Whoa

Anonymous at Tue, 4 Jun 2024 14:23:10 UTC No. 16209811

>>16209472
Can you make a geometric figure of this

Anonymous at Tue, 4 Jun 2024 16:39:26 UTC No. 16209985

>>16209759
>-1!=0!/0 ?
Guess what the gamma function does at every negative integer coordinate starting from 0.

Anonymous at Wed, 5 Jun 2024 05:02:47 UTC No. 16211084

>>16209811
Yes, it is the base geometric figure called a point, specifically the 0 point or origin point. it can be seen at the center of an empty 3d graph and spreads across each axis in lines and planes where zero perpetuates the other dimensions.

Anonymous at Wed, 5 Jun 2024 05:03:54 UTC No. 16211089

>>16209772
>the empty set has no elements
The empty set contains itself which can be arranged in exactly 1 way, how is that not an element?

Anonymous at Wed, 5 Jun 2024 08:16:15 UTC No. 16211200

>>16209467
>Is this science?
No, sorry, but it's off-topic

Anonymous at Wed, 5 Jun 2024 08:40:46 UTC No. 16211220

>>16211200
This board is for science and math, so while a raw math equation isn't science, it is not off-topic for the board either because it is math.

Anonymous at Wed, 5 Jun 2024 16:54:00 UTC No. 16212018

>>16211084
You know nothing about factorials.

Anonymous at Wed, 5 Jun 2024 16:55:13 UTC No. 16212019

>>16211200
You dont know how to read
Typical for a STEMCEL faggot btech indian kiddie

Anonymous at Wed, 5 Jun 2024 17:10:32 UTC No. 16212038

>>16211089
>The empty set contains itself
Is that an axiom or something that can be proved?
t. set-theory retard

Anonymous at Wed, 5 Jun 2024 18:47:00 UTC No. 16212169

>>16211089
The empty set contains no elements (but it does contain itself as a subset, because every element of the empty set is also an element of the empty set: this holds vacuously). The elements of the empty set can be put in order in a single way: this is again vacuously true.

>>16212038
See above, that anon is confusing the set membership relation [math]\in[/math] and the set inclusion relation [math]\subset[/math]. The claim "empty set contains itself (as a subset)" is trivially true.

Anonymous at Wed, 5 Jun 2024 19:13:46 UTC No. 16212210

>>16209472
Zero elements cannot be arranged at all.

Anonymous at Wed, 5 Jun 2024 19:28:31 UTC No. 16212218

>>16212210
The precise statement for "in how many ways can a set be arranged in" is "how many self-bijections of a set exist"? The only self-mapping of the empty set is the empty function, which is vacuously a bijection.

Anonymous at Wed, 5 Jun 2024 19:46:06 UTC No. 16212238

>>16212218
OP here that makes complete sense but it hurts my feelings so im gonna have a meltie

Anonymous at Wed, 5 Jun 2024 20:19:49 UTC No. 16212300

>>16212218
Well it's somewhat of slight of hand. It turns "zero" into "one" set (which is empty).

Anonymous at Wed, 5 Jun 2024 21:35:23 UTC No. 16212491

>>16209467
>Is this science?
No, ti's math and you're off-topic.

Anonymous at Thu, 6 Jun 2024 00:12:06 UTC No. 16212713

>>16212300
The empty set is still a set.

Anonymous at Thu, 6 Jun 2024 00:26:28 UTC No. 16212733

>>16212210

Anonymous at Thu, 6 Jun 2024 00:27:29 UTC No. 16212734

>>16209467
Science is a method to acquire knowledge. If you don't understand that then fuck off.

Anonymous at Thu, 6 Jun 2024 01:30:24 UTC No. 16212823

>>16211084
Gibberish

Anonymous at Thu, 6 Jun 2024 01:57:54 UTC No. 16212845

>>16212210
correct
>>16212733
retard

Anonymous at Thu, 6 Jun 2024 02:54:26 UTC No. 16212934

>>16209467
>science
It's math, not science. You fucking retard.

Anonymous at Thu, 6 Jun 2024 03:07:48 UTC No. 16212957

>>16212713
No it's not. It's bijected.

Anonymous at Thu, 6 Jun 2024 03:42:53 UTC No. 16213007

>>16211089
>The empty set contains itself
factually no
>>16212038
he's wrong, the empty set O={} is not the set containing the empty set {O}={{}}, the empty set containing nothing, while the set containing the empty set contain as one would guess, the empty set(which contains nothing), but the set containing the empty set IS the power set(https://en.wikipedia.org/wiki/Power_set ) of the empty set, so P(O)={O}

Anonymous at Thu, 6 Jun 2024 03:45:44 UTC No. 16213014

>>16213007
... these instances of "O" where meant to be [math]\varnothing[/math], it seems that 4chan filters the unicode version into "O", God knows what fuckery led to that decision

Anonymous at Thu, 6 Jun 2024 05:48:46 UTC No. 16213128

>>16212038
Law of Identity

Anonymous at Thu, 6 Jun 2024 05:50:57 UTC No. 16213129

>>16212210
An empty basket proves you wrong since the elements in it are arranged in exactly one way.

Anonymous at Thu, 6 Jun 2024 05:52:46 UTC No. 16213131

>>16212823
No, it is clearly a graph of an empty 3d field with the various sets of zero highlighted as planes.

Anonymous at Thu, 6 Jun 2024 05:55:51 UTC No. 16213133

>>16213007
nothing to the power of nothing isn't 0, though, its either 1 or left undefined
nothing times nothing is still just nothing, if you put an empty set in an empty set, the resulting set is still empty.

Anonymous at Fri, 7 Jun 2024 02:12:02 UTC No. 16218648

>>16213129
No. 'They' are not arranged because 'they' do not exist.

Anonymous at Fri, 7 Jun 2024 02:20:12 UTC No. 16218669

>>16212713
But zero isn't a set. A set containing zero isn't zero.

Anonymous at Fri, 7 Jun 2024 03:18:33 UTC No. 16218754

>>16213129
You're confusing "zero" with a container you've constructed in order to turn "zero" into "one." Stop this children's birthday party sleight of hand.

Anonymous at Fri, 7 Jun 2024 05:58:30 UTC No. 16218922

>>16218648
The stupid nerve of some people to come to a basket weaving forum just to claim that baskets don't exist.

Anonymous at Fri, 7 Jun 2024 05:59:24 UTC No. 16218923

>>16218754

how many different ways can you arrange no objects?

Anonymous at Fri, 7 Jun 2024 05:59:51 UTC No. 16218924

>>16218754
No, the empty set, zero, is a container which is why every integer is contained in an infinite field of 0s ..0001.000...

Anonymous at Fri, 7 Jun 2024 15:26:25 UTC No. 16219877

>>16218923
You cannot arrange no objects. "Arrangement" requires objects. It is a property of objects and isn't applicable to "no objects."

>the empty set, zero
Okay, so it's not zero. It's the empty set. How many sets do you have there? One, the empty set. You used "magic" to turn "zero" into "one."

Anonymous at Fri, 7 Jun 2024 16:45:22 UTC No. 16220048

>>16219877
forgot to tag:

>>16218924

Anonymous at Fri, 7 Jun 2024 18:29:45 UTC No. 16220266

>>16219877
You're literally making the no such thing as zero argument, but for elements of sets.

Define zero in such a way that it couldn't describe the number of elements in a set. Go ahead. I'll wait.

Anonymous at Fri, 7 Jun 2024 19:27:21 UTC No. 16220375

>>16220266
"zero' is a term for not having anything. There IS such a thing as the concept of "zero," but the actual thing, "zero" doesn't exist. It's the absence of something. You are not arranging anything since there's nothing that the action of "arrangement" can be imposed on.

Anonymous at Fri, 7 Jun 2024 20:05:42 UTC No. 16220450

>>16213131
A points has no magnitude or parts or dimension and sets of zero is fake and gay