>>>/g/52175281
Is he right, /sci/? I mean the parts about perfect circles and infinity not being real.
Circles are just edgy triangles.
Mathematical existence is independent from physical existence. We don’t know for sure if circles exist physically (given that the Plank length being the smallest distance possible is merely a popsci meme). As for infinity, there are many different forms of it:
A set is infinite if and only if there exists a bijection between it and itself with one element added. For instance, [math]\mathbf N^*[/math] is infinite because [math]\varphi:n \longmapsto n\,-\,1[/math] is a bijection between [math]\mathbf N^*[/math] and [math]\mathbf N[/math] (which is the same with 0 added).
A real sequence diverges towards positive infinity if and only if for any real number, the sequence eventually goes higher than it and always stays that way ([math]\forall A\in\mathbf R,\; \exists n_0\in\mathbf N,\; \forall n\in\mathbf N,\quad \mathrm{if}\,n\geq n_0,\,\mathrm{then}\,u_n \geq A[/math]).
Both these infinities are different and the symbol [math]\infty[/math] does not refer to any mathematical object. Saying infinity without referring to anything particular means jack shit.
>>7756245
of course they aren't "real". they are an abstraction, just like negative numbers, zero and essentially all of math.
saying perfect circles and infinity aren't "real" because you can't physically construct them and thinking your statement has any value makes you a simpleton retard
>>7756339
>how can circles be real when our maths aren't real
>>7756334
>the Plank length being the smallest distance possible is merely a popsci meme
nice one
>>7756334
You can't have an infinite number of things, it's impossible.
There should be a MAX_INT for math in real life.
The idea that something can go on forever is just wrong.
>>7756346
*if our i's aren't real
>>7756368
Wildburger pls go.
>>7756388
Never.
>>7756368
Without infinities, math is just arithmetic.
>>7756388
I'm serious, why would anyone want to use a number that is larger than, I don't know, lets say, the number of subatomic particles in the universe.
Is there a real world use for a number that goes higher than that?
>>7756450
bumping for curiosity
>>7756450
The number of combinations of subatomic particles.
>>7756467
Fine, the MAX_INT should be that, or can we go higher?
I just hate the idea of infinity, nothing can go on forever.
>>7756450
[math]e^{-\infty}[/math] is a lot easier to work with than [math]e^{-N_{sub. part.}}[/math]
>>7756482
We're not inside a computer, anon.
>>7756484
I like to pretend the "infinity" symbol is the MAX_INT symbol anyways.
>>7756489
>im
>fucking
>plying
>>7756489
So what?
>>7756482
MAX_INT + 1
Get wrekked faggot
>>7756482
>nothing can go on forever. [unreliable source][citation needed]
>>7756368
That's an interesting theory. Do you have evidence to back that up?
>>7756427
There are some ultrafinite approaches to math, but there actually really hard. The formalism alone is difficult since you can't formalize it in classical logic or even intuitionistic logic. There's been several attempts that have been shown to be insufficient at formalizing it. I read a paper on this that I can post if you're interested. It sounds very difficult to work in, IMO.
>>7756368
>There should be a MAX_INT for math in real life.
What benefit would that provide?
>>7756372
Kek
>>7756334
I agree that one should be careful with their wording, though arguably under the hood they're both the same set (everything is a set in set theory) so whether or not they're the same thing isn't so clean cut.
>A set is infinite if and only if...
You should be extremely careful to pont out that you are assuming the axiom of choice here. Without it you have over eight different reasonable definitions for an infinite set and they're all provably different (it's possible to interpret the set theory axioms in such a way that an infinite set of one type is not also an infinite set of another type). These definitions only agree with the axiom of choice. I can link a paper on this if you like.
I don't mind axiom of choice. I mean I can understand that in some cases a person will actually want to talk about some application where the axiom of choice makes sense (as opposed to the general case), but I do believe people should at least be aware of when they're using it. It's a very powerful statement with some very big repercussions, not mentioning it or even noticing it's there is just sloppy math.
>>7756641
Prove it.
>>7756450
Infinity is useful for many concepts in maths.
Calculus would be impossible without the notion of infinity.
Infinity was used in the proof demonstrating that not all problems are algorythmically solveable.
etc
>>7756641
>somewhere in that box is a perfect circle
No there isn't.
You can't even arrange atoms into a perfect circle.
>>7756482
how many points are in a line
>>7756334
gud
>>7756245
I depends really. Because if you think of say 1/x as x tends to infinity y tends to 0. Is that a 'Jew lie' cause all you're saying is if I keep moving further right along one axis the function will approach but never quite reach zero. So infinity is not a typical concept you really nee in everyday life but just because it's uncommon does'nt make it unreal.
>>7756635
>everything is a set in set theory
[pedant]Unless it's a proper class[/pedant]
>>7756368
>You can't have an infinite number of things, it's impossible.
>what are peano axioms
>>7756779
You're correct. I should have specified ZF or ZFC set theory. In NBG set theory we also have classes.
There's nothing wrong with being pedantic. Afterall, you can never be too correct.
>>7756782
Do you believe it makes sense to claim numbers exist in the Peano axiom system that are so large that you can't express them even by using all the subatomic particles in the universe?
>>7756811
>Do you believe it makes sense to claim numbers exist in the Peano axiom system that are so large that you can't express them even by using all the subatomic particles in the universe?
Math is detached from reality. We don't need to see if the axioms match the universe for them to make sense.
>>7756821
While that's true, these axiomatic systems are still formalized on top of formal languages over a finite alphabet where statements are strings of symbols. Can you rest assured that a number exists if you can't actually actually write it out formally? I mean the basic tenet by which we hold most of our proofs and arguments is that they're true because if someone really wanted to they could theoretically write down the formal details explicitly.
I'm not saying I disagree with you nor do I subscribe to the ultrafinitist perspective, but I just want to point out that the issue isn't as clear cut as "duh peano axioms".
>>7756844
The whole point of mathematics is to generalize problems and then give a general solution. If you come come with "but those aren't explciit solutions so we can't be 100% sure the deductions are correct" then we might as well give up at the beginning.
>>7756245
"God created the natural numbers; all the rest is the work of Man" -- L. Kronecker
imho it was a subtle anti-Jewish jab against Cantor
But ignoring that, I think he was basically right. The natural numbers are hard to argue with, and a lot of useful and complex things flow from them.
But the fact is that it is much more useful to make generalizations of the natural numbers. Negative numbers, fractions, irrational numbers, transcendental numbers -- none of these "exist" in any real sense. We've just been working with them for so long that we have internalized them perfectly and now they're natural for us.
Infinity is problematic just because that's the point at which generalizations break down and intuitions don't work so well.
I dunno why anyone would object to perfect circles, though. They're no less "real" than the square root of 2.
>>7756853
You misunderstood anon. The whole purpose of axiomatic systems and foundations in general are to give us a a rigorous formalism upon which to build. Most of mathematicians work informally (they aren't referencing any axioms or detailing every logical step) and the way this is justified is by claiming that they're implicitly using a foundation and that their informal arguments could be completely formalized within this foundation if one wanted to.
For instance, one might prove a bunch of theorems regarding homotopy in topology without ever saying if they're working in ZFC or Category Theory or whatever. However implicitly there's a belief that if you wanted to you could formalize their statements in ZFC (for instance) explicitly. This does not mean that the statement is less general nor that it can even be generalized by not writing out the details. This is entirely a question of utter rigor and formalism.
On a completely separate note, I would also argue that generalization isn't the purpose of mathematics since we often have some goal in mind while working and it is often possible to generalize a concept in more than one way. In this sense it can introduce a lot of wasted effort (spending days generalizing a proof to a level you will never need, or generalizing things in one way only to later rebuild the theory because you need it a different way). That said it is still very important and useful.
There are also many parallels to programming. Here is an argument in that context.
https://medium.com/@fredriknoren/on-generalization-608949214e63
How many countable things are there in the universe, /sci/?
And don't tell me it's infinite.
>>7756245
Yep.
>>7756600
It would make math more understandable and complete, irrational numbers like pi would become rational as they wouldn't have to go on for infinity, they would stop at the point where it's physically impossible for them to exist.
>>7756368
Think of infinity as "as big as you want" instead of "going on forever" and this will save you a lot of brain farts.
>>7758277
Something can only be so big, anon. It's literally the same thing.
>>7756368
OK, say you have a finite number of things.
I now divide them all in half. How many things do you have?
>>7756589
>I don't believe in god. [unreliable source][citation needed]
It's on you to prove the existence of infinity, m8.
>>7756596
https://en.wikipedia.org/wiki/Cyclic_model
What about this?
>>7758446
Infinities exist in our intuition for example in the form of the natural numbers. We can not prove things without starting from somewhere so we make axioms. The axioms of ZFC for example, follow our intuition nicely so we like them and use them. Assuming the axioms of ZFC we can prove the existence of infinite sets and even infinite sets of different "sizes". (Although you may want to know that the existence of an infinite set is actually an axiom of ZFC.)
>>7758472
There are only a finite number of things we can count.
Tell me something that is non-abstract and infinite.
>>7758428
>biologist here to make an arse of himself
No surprise
>>7756450
>implying science has concrete evidence (besides mathematical theorems) to prove that the universe is finite, and therefore a finite number of subatomic particles exist
>>7758528
>implying science has concrete evidence (besides mathematical theorems) to prove that the universe is infinite, and therefore an infinite number of subatomic particles exist
>>7756450
The power set of the particles in the observable universe. Then the power set of the original power set unioned with the original set or just the power set of the power set. Then the power set of that. It doesn't fucking matter how you choose it. There's always some way to produce a higher number than the one you described using a finite number of starting elements.
>>7758397
The one good counter example is ignored, of course
>>7758446
I'm not saying infinity exists, I'm just a new replier saying that the naturals exist, and they have a certain size.
>>7758495
New replier here! Distance and future time. The elements produced by repeated application of the power set operation for any finite set of elements.
>>7756450
> I don't even know Calculus: the post
>>7758630
Calculus is just another meme.
I also want to have max_int in math or at least a variable for an upper limit
can't we just split math in to engineering maths and philosophical maths already
>>7758736
Pure applied
>>7758397
There's no evidence that you can't divide something over and over.
>>7756368
Infinity doesn't only refer to "counting," but more generally to "quantity." I've heard astronomers refer to collapsed stars as "infinitely dense" because the mass:volume ratio is insanely high.
>>7756245
They are not necessarily unreal, but you can never know for sure if you have found some.
