So what about an `infinite set'? Well, to begin with, you should say precisely what the term means. Okay, if you don't, at least someone should. Putting an adjective in front of a noun does not in itself make a mathematical concept. Cantor declared that an `infinite set' is a set which is not finite. Surely that is unsatisfactory, as Cantor no doubt suspected himself. It's like declaring that an `all-seeing Leprechaun' is a Leprechaun which can see everything. Or an `unstoppable mouse' is a mouse which cannot be stopped. These grammatical constructions do not create concepts, except perhaps in a literary or poetic sense. It is not clear that there are any sets that are not finite, just as it is not clear that there are any Leprechauns which can see everything, or that there are mice that cannot be stopped. Certainly in science there is no reason to suppose that `infinite sets' exist. Are there an infinite number of quarks or electrons in the universe? If physicists had to hazard a guess, I am confident the majority would say: No. But even if there were an infinite number of electrons, it is unreasonable to suppose that you can get an infinite number of them all together as a single `data object'.
So what about an `infinite set'? Well, to begin with, you should say precisely what the term means. Okay, if you don't...
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infinites are dumb
most of modern math is dumb
that's not going to change unless smart people who can see that fact invent new and better math
so get started or shut up
UM I'LL TAKE A CHEESEBURGER, NO PICKLES, LARGE FRIES AND A DIET COKE
...
There's literally nothing wrong with infinite sets. Axiom of choice on the other hand...
show me something in reality that can be modeled by an infinite set
oh wait
>hurr durr practical application is the basis for mathematical legitimacy
[math]\forall x,y \in N \exists y > x[/math]
[math]Suppose n=x, then y=n+1[\math]
This follows by definition from the Peano axioms. The set of natural numbers has no maximum upward boundary. This means that no matter what whole number you think of there is always a larger one in the set. How do you define infinite? Would you say boundless is one way?
Amplifiers
If a part of mathematics doesn't correspond to something in reality it is useless and unprovable. Infinite sets make just as much sense as 1 = 4.
The problem is you don't want to look at math.
Let us look at your problem then.
How does a finite thing bound itself?
If you have an infinite set and you want to shift all items down by one, you'd have to coordinate them all to move at the same time. This isn't possible unless you are God. Mathematicians are playing god with their satanic formulae and should tread very carefully.
No, the problem is that you have decided any internally consistent concept MUST be valid math.
completely false, mathematics does one thing and one thing only, study the consequences of assumed axioms, choosing those axioms to coincide with the laws of the world we live in is the realm of science.
>show me something in reality that can be modeled by an infinite set
Literally everything in reality can be modeled by an infinite set. A thing doesn't need to be physically infinite to be capable of being modeled by a conceptual infinity.
...
things are provable in respect to certain axioms not in some universal sense, just because you don't like a certain axiomatic system because it seems too different from your world doesn't make it any more or less capable of rigorous mathematics
so again you are arbitrarily deciding that "validity" comes from practical application.
>show me something in reality that can be modeled by an infinite set
The set of possible distances between two objects
Mathematics that do not correspond to reality are worthless fiction. There are an infinite number of internally consistent systems with no correspondence to reality. Are they all valid math to you?
>Are they all valid math to you?
Of course, do you not know what valid means?
Absolutely, any differentiation you make based on how close something resembles our universe is arbitrary by definition.
loling @ your life
no wonder nobody takes mathematicians seriously
>loling @ your life
>no wonder nobody takes mathematicians seriously
en.wikipedia.org
What does a troll know of the universe anyway.
You should find better topics which aren't so easily refuted so you aren't ignored after 20 posts.
People who actually think the only mathematics which are valid are the ones that apply to our universe shouldn't be pursuing a career in mathematics in the first place.
What's the difference between abstract math and abstract philosophy in that regard?
All math is philosophy, but not all philosophy is math.
Just because nobody at your Jiffy Lube takes mathematics seriously doesn't mean people don't take mathematics seriously.
mathematics makes assumptions, axioms, and examines the formal consequences of them, nothing more. Philosophy is less rigorous and actually concerned with our universe much more than mathematics.
Anything internally consistent is real and useful guise.
Why the fuck do you post this twoce a wekk? Whats up with that?
"valid" = "useful"
why do people keep responding
I'm not that guy
>axioms are hard, someone make some better ones
>kay thanks bye
>I'm not that guy
I'm not a "guy".
>you'd have to coordinate them all to move at the same time. This isn't possible unless you are God.
[CITATION NEEDED]
Are you claiming to be able to calculate something which requires infinite processing power?
I dont know man, at least remember to sage, please.
No, retard.
The comment im responding to made a very specific cliam as it were fact without any basis. They need show evidence for that claim.
so you are saying you (or someone) can do it
good to know, heretic
No im not, how can you possibly be this dense? Leave this board, never come back.
>interacting with an infinite number of things doesn't require infinite processing power
top brainlet
Holy shit you filthy mongoloid, no one ever made that claim or implied that to be true, the original response asked for citation for the claim made in the comment they were responding to. All of you done is attempt to strawman.
(((Wildberger)))
(((Zeilberger)))
There's a pattern here...
Literally anything with curves.
Achilles catching up with the tortoise.
that's not reality brainlets
those are models of things that really happen
>So what about an `infinite set'?
Well, to begin with, you should have a verb in your question, faggot.
show me someone ignorant of modelling
oh wait...
>nobody takes mathematicians seriously
...in your odd little inner world.
>Well, to begin with, you should have a verb in your question, faggot.
Why the homophobia?
>things in my abstract apriori number game have to "correspond" to reality
1=4 in any field of characteristic 3
the continuum