[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]

2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

File: 10 KB, 320x240, tmp_10161-197455201003202-818149835.jpg [View same] [iqdb] [saucenao] [google]

9434555

Anonymous Sat Jan 13 12:38:38 2018 No.9434555 [Reply] [Original]

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'.

>>	Anonymous Sat Jan 13 12:50:36 2018 No.9434581 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

>>	Anonymous Sat Jan 13 12:54:56 2018 No.9434586 >>9434555 UM I'LL TAKE A CHEESEBURGER, NO PICKLES, LARGE FRIES AND A DIET COKE

>>	Anonymous Sat Jan 13 12:55:09 2018 No.9434587 File: 34 KB, 200x279, wildburger.jpg [View same] [iqdb] [saucenao] [google] >>9434581

>>	Anonymous Sat Jan 13 12:55:53 2018 No.9434589 There's literally nothing wrong with infinite sets. Axiom of choice on the other hand...

>>	Anonymous Sat Jan 13 12:58:49 2018 No.9434595 >>9434589 show me something in reality that can be modeled by an infinite set oh wait

>>	Anonymous Sat Jan 13 13:04:04 2018 No.9434607 >>9434595 >>9434581 >hurr durr practical application is the basis for mathematical legitimacy

>>

Anonymous Sat Jan 13 13:04:48 2018 No.9434610

>>9434555
>>9434555
[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?

>>9434595
Amplifiers

>>	Anonymous Sat Jan 13 13:09:00 2018 No.9434618 >>9434607 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.

>>	Anonymous Sat Jan 13 13:10:31 2018 No.9434619 >>9434618 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?

>>

Anonymous Sat Jan 13 13:11:43 2018 No.9434622
File: 167 KB, 480x640, sicp.jpg [View same] [iqdb] [saucenao] [google]

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.

>>	Anonymous Sat Jan 13 13:11:51 2018 No.9434623 >>9434619 No, the problem is that you have decided any internally consistent concept MUST be valid math.

>>	Anonymous Sat Jan 13 13:12:45 2018 No.9434627 >>9434618 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.

>>	Anonymous Sat Jan 13 13:13:50 2018 No.9434629 >>9434595 >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.

>>	Anonymous Sat Jan 13 13:14:01 2018 No.9434630 >>9434627 >>9434623

>>

Anonymous Sat Jan 13 13:14:33 2018 No.9434631

>>9434618
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

>>	Anonymous Sat Jan 13 13:15:52 2018 No.9434637 >>9434623 so again you are arbitrarily deciding that "validity" comes from practical application.

>>	Anonymous Sat Jan 13 13:17:24 2018 No.9434645 >>9434595 >show me something in reality that can be modeled by an infinite set The set of possible distances between two objects

>>	Anonymous Sat Jan 13 13:18:38 2018 No.9434649 >>9434631 >>9434637 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?

>>	Anonymous Sat Jan 13 13:19:22 2018 No.9434650 >>9434649 >Are they all valid math to you? Of course, do you not know what valid means?

>>	Anonymous Sat Jan 13 13:20:14 2018 No.9434654 >>9434649 Absolutely, any differentiation you make based on how close something resembles our universe is arbitrary by definition.

>>	Anonymous Sat Jan 13 13:21:05 2018 No.9434657 >>9434650 >>9434654 loling @ your life no wonder nobody takes mathematicians seriously

>>	Anonymous Sat Jan 13 13:21:29 2018 No.9434658 >>9434657 >loling @ your life >no wonder nobody takes mathematicians seriously https://en.wikipedia.org/wiki/Validity

>>	Anonymous Sat Jan 13 13:23:03 2018 No.9434659 >>9434657 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.

>>	Anonymous Sat Jan 13 13:23:06 2018 No.9434660 >>9434657 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.

>>	Anonymous Sat Jan 13 13:25:48 2018 No.9434663 >>9434660 What's the difference between abstract math and abstract philosophy in that regard?

>>	Anonymous Sat Jan 13 13:27:01 2018 No.9434666 >>9434663 All math is philosophy, but not all philosophy is math.

>>	Anonymous Sat Jan 13 13:27:26 2018 No.9434667 >>9434657 Just because nobody at your Jiffy Lube takes mathematics seriously doesn't mean people don't take mathematics seriously.

>>	Anonymous Sat Jan 13 13:28:17 2018 No.9434669 >>9434663 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.

>>	Anonymous Sat Jan 13 13:29:20 2018 No.9434672 File: 81 KB, 645x729, 1515704051190.jpg [View same] [iqdb] [saucenao] [google] Anything internally consistent is real and useful guise.

>>	Anonymous Sat Jan 13 13:29:35 2018 No.9434674 >>9434555 Why the fuck do you post this twoce a wekk? Whats up with that?

>>	Anonymous Sat Jan 13 13:30:04 2018 No.9434676 File: 12 KB, 210x239, daniel.png [View same] [iqdb] [saucenao] [google] >>9434672 "valid" = "useful"

>>	Anonymous Sat Jan 13 13:30:22 2018 No.9434678 >>9434674 why do people keep responding

>>	Anonymous Sat Jan 13 13:31:24 2018 No.9434680 >>9434676 I'm not that guy

>>	Anonymous Sat Jan 13 13:31:36 2018 No.9434681 >>9434581 >axioms are hard, someone make some better ones >kay thanks bye

>>	Anonymous Sat Jan 13 13:33:58 2018 No.9434685 >>9434680 >I'm not that guy I'm not a "guy".

>>	Anonymous Sat Jan 13 13:35:18 2018 No.9434689 >>9434622 >you'd have to coordinate them all to move at the same time. This isn't possible unless you are God. [CITATION NEEDED]

>>	Anonymous Sat Jan 13 13:36:25 2018 No.9434692 >>9434689 Are you claiming to be able to calculate something which requires infinite processing power?

>>	Anonymous Sat Jan 13 13:38:21 2018 No.9434698 >>9434678 I dont know man, at least remember to sage, please.

>>	Anonymous Sat Jan 13 13:40:18 2018 No.9434705 >>9434692 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.

>>	Anonymous Sat Jan 13 13:41:11 2018 No.9434706 >>9434705 so you are saying you (or someone) can do it good to know, heretic

>>	Anonymous Sat Jan 13 13:46:42 2018 No.9434722 >>9434706 No im not, how can you possibly be this dense? Leave this board, never come back.

>>	Anonymous Sat Jan 13 13:47:32 2018 No.9434725 >>9434722 >interacting with an infinite number of things doesn't require infinite processing power top brainlet

>>	Anonymous Sat Jan 13 14:54:04 2018 No.9434866 >>9434725 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.

>>	LeSage Sat Jan 13 15:28:17 2018 No.9434934 >>9434587 (((Wildberger))) (((Zeilberger))) There's a pattern here...

>>	Anonymous Sat Jan 13 15:39:41 2018 No.9434965 >>9434595 Literally anything with curves.

>>	Anonymous Sat Jan 13 18:50:23 2018 No.9435485 >>9434595 Achilles catching up with the tortoise.

>>	Anonymous Sat Jan 13 21:18:13 2018 No.9435833 >>9434965 >>9435485 that's not reality brainlets those are models of things that really happen

>>	Anonymous Sat Jan 13 21:27:25 2018 No.9435848 >>9434555 >So what about an `infinite set'? Well, to begin with, you should have a verb in your question, faggot.

>>	Anonymous Sat Jan 13 21:29:50 2018 No.9435850 >>9434595 show me someone ignorant of modelling oh wait...

>>	Anonymous Sat Jan 13 21:35:17 2018 No.9435858 >>9434657 >nobody takes mathematicians seriously ...in your odd little inner world.

>>	Anonymous Sat Jan 13 21:36:12 2018 No.9435862 >>9435848 >Well, to begin with, you should have a verb in your question, faggot. Why the homophobia?

>>	Anonymous Sat Jan 13 21:37:39 2018 No.9435864 >>9434555 >things in my abstract apriori number game have to "correspond" to reality

>>	Anonymous Sun Jan 14 00:00:02 2018 No.9436146 >>9434618 1=4 in any field of characteristic 3

>>	Anonymous Sun Jan 14 00:52:25 2018 No.9436212 >>9434595 the continuum