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No.10200056 [Reply] [Original] [archived.moe]

Would any finitist attempt to explain the problems with
>infinity
>uncountable sets
>ZFC
WITHOUT falling back onto "I've never seen infinity" or any other argument that is predicated on empirical observation or anything in "this universe" as a reason?

 >> Anonymous Sat Dec 8 17:26:18 2018 No.10200083 >>10200056>Implying that you'll find people that are nearly educated enough (ultra)finitists here
 >> Anonymous Sat Dec 8 17:41:38 2018 No.10200119 >>10200056Infinity is the linked set's values that are unrelated for the operation being performed on a discrete/distinct object.Infinity is just the extra fluff in the mashmallow, the buffer that allows you abstractly pierce a set non-destructively.Infinity = unreferenced/unfilled space.
 >> Anonymous Sat Dec 8 17:46:24 2018 No.10200133 >>10200056fuck off. the universe is discrete
 >> Anonymous Sat Dec 8 17:47:57 2018 No.10200137 >>10200133The universe is a subset of mathmatical infinity.
 >> Anonymous Sat Dec 8 17:48:09 2018 No.10200139 >>10200119>Infinity is the linked set's values that are unrelated for the operation being performed on a discrete/distinct object.That's fine, so what? >>10200133Completely irrelevant
 >> Anonymous Sat Dec 8 17:49:11 2018 No.10200143 >>10200133>muh planck length
 >> Anonymous Sat Dec 8 17:51:43 2018 No.10200152 >>10200139They aren't problems. OP's premise is flawed.
 >> Anonymous Sat Dec 8 17:54:52 2018 No.10200161 >>10200152>OP's premise is flawed.No it isn't
 >> Anonymous Sat Dec 8 17:56:41 2018 No.10200167 >>10200056It isn't possible to talk about "infinity" without instantly misrepresenting it, because you have to treat it like a finite "thing" in order to even conceptualise or represent it in the first place.With that said, "infinity" "exists", but not like finite things exist, therefore infinitists who accept its "existence" are correct, but wrong to try and use it as a finite "thing".Finitists who deny that "infinity" "exists" are correct in the sense of it not existing as a finite thing, but wrong to outright deny it at all.
 >> Anonymous Sat Dec 8 17:57:44 2018 No.10200171 >>10200167>It isn't possible to talk about "infinity" without instantly misrepresenting it, because you have to treat it like a finite "thing" in order to even conceptualise or represent it in the first place.Why is this the case?
 >> Anonymous Sat Dec 8 17:58:06 2018 No.10200173 >>10200161You don't want to listen to mine or your own so I obviously am not the one you would accept satisfaction from.
 >> Anonymous Sat Dec 8 17:59:08 2018 No.10200175 >>10200167You are mixing up 'uncountable source of x' with 'expansion to allow x -> y'
 >> Anonymous Sat Dec 8 18:02:57 2018 No.10200182 >>10200119basically this. in nonstandard analysis its no longer mysterious, infinity is just whats outside of the scope of what youre looking at (one order up) and infinitesmals are one order down, like the difference between counting atoms and counting apples, and counting apples and counting countries
 >> Anonymous Sat Dec 8 18:04:13 2018 No.10200187 >>10200167You're just using words without understanding what they mean. This is equivalent to saying we can't represent an unknown quantity accurately because if you set it to X, you're already assuming it's known.
 >> Anonymous Sat Dec 8 18:07:05 2018 No.10200197 >>10200171Because it's the equivalent of trying to define/conceptualise "nothing".
 >> Anonymous Sat Dec 8 18:07:51 2018 No.10200202 >>10200175Expansion is a finite property.
 >> Anonymous Sat Dec 8 18:09:20 2018 No.10200210 >>10200187>if you set it to X, you're already assuming it's knownKnown in what way?
 >> Anonymous Sat Dec 8 18:09:29 2018 No.10200211 >>10200056>debating nominalists>as if infinity is the biggest problem, not truth or nominalism itself>" As such, he claims, our organs, as part of this world, would by implication also be the work of our organs. Unless then we are to assume that the concept of a causa sui is not an absurd one, the external world is, reduction ad absurdum, not the work of our organs"
 >> Anonymous Sat Dec 8 18:09:39 2018 No.10200213
 >> Anonymous Sat Dec 8 18:14:13 2018 No.10200225
 >> Anonymous Sat Dec 8 18:15:52 2018 No.10200230 >>10200202Expansion yes, successor functions no
 >> Anonymous Sat Dec 8 18:16:17 2018 No.10200232 >>10200225It was supposed to be the null set.Anyway, here is nothing: {}not hard to define or conceptualize
 >> Anonymous Sat Dec 8 18:20:57 2018 No.10200238 >>10200230A quantity of successor functions?
 >> Anonymous Sat Dec 8 18:21:28 2018 No.10200240 >>10200232>Anyway, here is nothing: {}I see brackets? Brackets are something.
 >> Anonymous Sat Dec 8 19:35:29 2018 No.10200363 >>10200238+1 until failure
 >> Anonymous Sat Dec 8 19:50:12 2018 No.10200408 File: 13 KB, 1000x294, lamp.gif [View same] [iqdb] [saucenao] [google] [report] >>10200056Suppose I had a lamp at time t = 0, then at time t = 2^(-n) for every single n natural number I flipped the switch of the lamp, every time I flip the switch if it is on it turns off and if it is off it turns on. The lamp is off at t = 0.What is the state of the lamp at t = 1?The correct answer is that this situation is impossible, we then ask why it is impossible, the answer is that we cannot have infinities. (inb4 brainlet answers like that physics doesn't allow lamps that can change at arbitrarily fast speeds)
 >> Anonymous Sat Dec 8 19:50:24 2018 No.10200410 >>10200363>+1 until failurewat
 >> Anonymous Sat Dec 8 20:04:39 2018 No.10200444 >>10200240you should honestly jump off a bridge
 >> Anonymous Sat Dec 8 20:08:09 2018 No.10200452 >>10200056I do not assume the axiom of infinity.The burden of proof lies on you to explain why I should.
 >> Anonymous Sat Dec 8 20:13:00 2018 No.10200458 >>10200444no ur mom
 >> Anonymous Sat Dec 8 20:13:26 2018 No.10200460 >>10200408>The correct answer is that this situation is impossible, we then ask why it is impossible, the answer is that we cannot have infinities.conclusion doesnt follow from the premisesyou havent demonstrated a problem with infinity>>10200452>literally just ignoring the question and acting like youre smart for being a coward
 >> Anonymous Sat Dec 8 20:14:36 2018 No.10200463 >>10200452No, the burden of proof is on you to show me which natural number is the largest
 >> Anonymous Sat Dec 8 20:17:28 2018 No.10200470
 >> Anonymous Sat Dec 8 20:22:00 2018 No.10200481 File: 56 KB, 192x154, 312452346.png [View same] [iqdb] [saucenao] [google] [report] >>10200460>implying questioning the assumptions behind the question is ignoring the question
 >> Anonymous Sat Dec 8 20:54:13 2018 No.10200556 File: 103 KB, 1416x944, P.jpg [View same] [iqdb] [saucenao] [google] [report] >>10200056The only thing in some sense outside "this universe" that could be a problem with ZFC would be proving that ZFC contradicts itself in purely logical terms.Since noone has found a purely logical contradiction in ZFC all objections are based on either observation or adding extra logical assumptions.What you're asking for doesn't exist.
 >> Anonymous Sat Dec 8 20:55:25 2018 No.10200560 >>10200481>implying theres a coherent way to question the assumption>"theres a largest finite set of size N"N+1gger
 >> Anonymous Sun Dec 9 03:52:53 2018 No.10201333 >>10200056No infinity - no problems.
 >> Anonymous Sun Dec 9 08:40:50 2018 No.10201694 >>10201333but there is an infinity (multiple, actually) so try again
 >> Anonymous Sun Dec 9 09:14:19 2018 No.10201751 >>10201694Source: your ass.If there's infinity, then tell me the infinith digit of pi.
 >> Anonymous Sun Dec 9 09:23:51 2018 No.10201758 >>10201751>Source: your ass.Nope, if you want to claim there NUMBERS ARE FINITE (I can't even begin to understand how a stupid a sniveling moron must be to entertain such a concept) then what is the largest natural number.>If there's infinity, then tell me the infinith digit of pi.This is not a retort, this is implying there is one. The whole point is that there IS NO END. There is no "infinith" term or digit or number, as then it wouldn't be infinite. That's the point.
 >> Anonymous Sun Dec 9 09:33:56 2018 No.10201777 File: 161 KB, 1024x1024, wnxxbwroui221.jpg [View same] [iqdb] [saucenao] [google] [report] >>10200056> WITHOUT falling back onto "I've never seen infinity"That is all there is to the argument though, isn't it?If mathematics is supposed to be isomorphic to things in the real world (which is a reasonable demand as we use mathematics to make real-world predictions), then it would be the safer bet to restrict yourself to finite/discrete objects because the underlying quantum graph appears to be such an object, especially since the alternative cannot be proven to be consistent.
 >> Anonymous Sun Dec 9 09:38:23 2018 No.10201785 >>10201758>NUMBERS ARE FINITEYes? Take any number, it's finite.>This is not a retort, this is implying there is one.Yes, the digit at the infinith position. It relies on existence of infinity. If there's no infinity, then there's no infinith position, yes.>The whole point is that there IS NO END.In other words, no infinity.>There is no "infinith" term or digit or number, as then it wouldn't be infinite.So if infinity existed then it wouldn't be infinite. That's why it doesn't exist.
 >> Anonymous Sun Dec 9 09:39:17 2018 No.10201788 >>10201777>If mathematics is supposed to be isomorphicIt isn't though. It is beyond this world.Of course this world would be constrained by the laws of math. But math is in NO WAY constrained to the laws of this universe.Once you understand this, there is no confusion. >especially since the alternative cannot be proven to be consistent.It CAN be proven to be consistent, it just must never be finite. So there must exist an infinite ideal realm that is non spatial and non temporal that objectively exists in which all math resides. Plato was literally right (LITERALLY right) and there objectively and externally exists an infinite ideal realm.
 >> Anonymous Sun Dec 9 09:40:23 2018 No.10201790 File: 6 KB, 211x239, 1512340048154.png [View same] [iqdb] [saucenao] [google] [report] >>10201785 (you)
 >> Anonymous Sun Dec 9 09:47:27 2018 No.10201797 The x be the largest positive integer(x+1) > x ContradictionTherefore, there is no largest positive integer.QED
 >> Anonymous Sun Dec 9 10:06:56 2018 No.10201829 >>10201785You didn't tell him what the largest number is What is the largest number?>>10201797This
 >> Anonymous Sun Dec 9 10:17:43 2018 No.10201850   $\mathscr{P}(\mathbb{C})$Now what, fags?
 >> Anonymous Sun Dec 9 10:21:25 2018 No.10201859 $\mathscr{P} ( \mathbb{C} )$Now what, fags?
 >> Anonymous Sun Dec 9 10:33:04 2018 No.10201883 File: 195 KB, 1650x1050, 1488360386615.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sun Dec 9 10:35:15 2018 No.10201886 >>10200167How is it treated like a finite thing incorrectly?
 >> Anonymous Sun Dec 9 10:42:34 2018 No.10201895 >>10200408On, since 2^(-0) = 1. 0 is the first natural number, so the first time you switch the lamp is at t = 1.
 >> Anonymous Sun Dec 9 10:50:33 2018 No.10201908 File: 36 KB, 457x459, Dg3DxoQX0AAPquU.jpg [View same] [iqdb] [saucenao] [google] [report] >>10201785>>This is not a retort, this is implying there is one.>Yes, the digit at the infinith position. It relies on existence of infinity. If there's no infinity, then there's no infinith position, yes.>>The whole point is that there IS NO END.>In other words, no infinity.youre trying to treat infinity as if its a finite numberif the digits had an end they would be finiteif the digits had no end they would be infinite.this is really fucking simple, so you cant take the "last digit" of something with an infinite number of digits"Infinity is a size, the size of something that doesn't end" -Vsauce, Micheal Here
 >> Anonymous Sun Dec 9 11:03:55 2018 No.10201932 >>10201777I see what is going on here. The anon realized that mathematics was all about exploring the limits of the human mind and he wasn't smart enough of that. Then he saw physics as something that just explores the limits of the universe. Something much simpler. Even a monkey could be a physicist, I hope we can all agree on that. So now this anon, salty and butthurt, wants to downgrade mathematics to something that explores the limits of the universe, like some kind of weird and pointless abstracted physics. No thank you, just because you are too stupid for math doesn't mean you get to downgrade all of us with you.
 >> Anonymous Sun Dec 9 11:18:31 2018 No.10201956 >>10201932Lmao this
 >> Anonymous Sun Dec 9 11:27:34 2018 No.10201968 >>10201788> But math is in NO WAY constrained to the laws of this universe.We are free to decide what we call math and what we want to spend our time on. You are right that the set of all formal languages goes beyond the laws of nature, but the question is whether it is useful to study things that bear no resemblence to the quantum graph.>>10201932Nope. Even some physicists are considering this possibility, see e.g. section VII. C in this paper:https://arxiv.org/pdf/0704.0646.pdfThe restriction to finite objects also rather makes math HARDER, not easier, e.g. it becomes harder to define limits and some proofs become harder as you cannot rely on assumptions of non-existence.
 >> Anonymous Sun Dec 9 11:28:19 2018 No.10201969 >>10200408You fucked up the problem but the answer is that any defined change has a nonzero amount of time to take place. The amount of time it takes to switch from on to off determines the state of the switch.
 >> Anonymous Sun Dec 9 11:34:05 2018 No.10201975 >>10201859>using \mathscr{P} instead of \wp for the powerset
 >> Anonymous Sun Dec 9 11:35:57 2018 No.10201976 >>10201751There is none, all digits of pi correspond to a natural number.
 >> Anonymous Sun Dec 9 11:39:09 2018 No.10201982 >>10201777Physics uses infinity, infinite numbers, limits, calculus, etc. so your assumption that only finite objects correspond to reality is empirically false.
 >> Anonymous Sun Dec 9 11:44:45 2018 No.10201993 >>10201751>if there is no last digit of pi, then tell me the last digit of piThis is your brain on finitism.
 >> Anonymous Sun Dec 9 11:46:45 2018 No.10201997 >>10201975Here's what I usually use (piss poor spam detection):https://pastebin.com/dFxfWNrBBut yeah, maybe I did pick poorly.$\wp{ ( \mathbb{C} ) }$
 >> Anonymous Sun Dec 9 11:50:30 2018 No.10202005 >>10200133time
 >> Anonymous Sun Dec 9 12:02:45 2018 No.10202054 >>10201829nah, 10201798 is larger
 >> Anonymous Sun Dec 9 20:48:04 2018 No.10203458 >>10200056I agree completely. I don't care that there might be a finite number of particles in existence. Infinity is an elegant and useful concept. It really doesn't matter than you've never been able to count to it.
 >> Anonymous Sun Dec 9 20:49:18 2018 No.10203463 >>10200133So is time not finite? How exactly does Time begin and end?
 >> Anonymous Sun Dec 9 22:23:29 2018 No.10203681 >>10201982No physical processes are known that perform infinitely many steps at once. Whenever we use infinities or limits in physics, we could in principle also use finite approximations thereof.
 >> Anonymous Sun Dec 9 22:38:18 2018 No.10203721 >>10203681>No physical processes are known that perform infinitely many steps at once.How does that respond to my post?>Whenever we use infinities or limits in physics, we could in principle also use finite approximations thereof.Finite approximations of what?
 >> Anonymous Sun Dec 9 22:40:05 2018 No.10203725 >>10203721>How does that respond to my post?How does that respond to my post?>Finite approximations of what?thereof.
 >> Anonymous Sun Dec 9 22:44:20 2018 No.10203737 >>10203725>How does that respond to my post?Your claim is an irrelevancy. Infinity is used in empirically proven physics.>thereof.What is thereof? The real constants? Because if you can only approximate the real constants with finite math then you are admitting that infinite math better describes reality.
 >> Anonymous Sun Dec 9 22:47:02 2018 No.10203744 >>10200167what you are trying to articulate is the distinction between actual and potential infinity. The potentially infinite, unfortunately, is not ontic, and that's really all that matters in this discussion. Finitism has always the potential to be wrong, but never will be because you'll never reach an actual infinity. Isn't that funny?
 >> Anonymous Sun Dec 9 22:47:04 2018 No.10203745 >>10203737>Your claim is an irrelevancy. Infinity is used in empirically proven physics.How does that respond to my post?>What is thereof? The real constants? Because if you can only approximate the real constants with finite math then you are admitting that infinite math better describes reality.No, just thereof.
 >> Anonymous Sun Dec 9 22:54:25 2018 No.10203763 File: 41 KB, 562x437, haha.jpg [View same] [iqdb] [saucenao] [google] [report] >>10203745Oh look it's another finitard reduced to shitposting after getting BTFO.
 >> Anonymous Sun Dec 9 22:55:19 2018 No.10203767 >>10203763>t. brainlet
 >> Anonymous Sun Dec 9 22:56:48 2018 No.10203769 >>10203721>How does that respond to my post?You said physicists use infinities and limits (computations with infinitely many steps) to describe things in the universe. However, the things they describe do not make these infinitely many steps explicitly visible. We do not know whether physical processes actually perform infinitely many steps, we only know that our predictions on infinitist axioms they match well. However that is an underdetermined theory, i.e. there are alternative models that fit just as well, namely finite approximations.In addition, we have plenty of evidence of a discrete quantum graph, but NO good evidence of infinities, e.g. no infinitely dense or hot things. Conversely, axiom systems involving infinities have dreadful theoretical issues like uncomputability/undecideability, counterintuitive results like nondenumerability, Banach-Tarski. I'd say finite theories are backed up by more evidence and are nicer in many ways, so they should be preferred.>Finite approximations of what?E.g. very large numbers instead of infinities or a truncated sum instead of an infinite one.
 >> El Arcón Sun Dec 9 22:57:22 2018 No.10203771 >>10200056I've never seen 2^{10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}Does that mean it doesn't exist? I've never 25 hippos either. Do 25 hippos exist?
 >> Anonymous Sun Dec 9 23:00:03 2018 No.10203778 >>10203737>Your claim is an irrelevancy. Infinity is used in empirically proven physics.So are numbers. Are those real? Mathematical machinery used to construct theories are just that, and to say that their usage implies their reality is a philosophical step too far. You can believe it if you want, but don't pretend it's physics
 >> Anonymous Sun Dec 9 23:35:37 2018 No.10203837 >>10203769>You said physicists use infinities and limits (computations with infinitely many steps) to describe things in the universe. However, the things they describe do not make these infinitely many steps explicitly visible. We do not know whether physical processes actually perform infinitely many steps, we only know that our predictions on infinitist axioms they match well. I was responding to the claim that nonfinite mathematics does not correspond to reality, so saying that some specific thing is not "visible" is irrelevant of you admit that physics uses infinity in many ways.>However that is an underdetermined theory, i.e. there are alternative models that fit just as well, namely finite approximations.If they are approximations then by definition they don't fit "just as well.">In addition, we have plenty of evidence of a discrete quantum graph, What about quantum graphs with infinite or semi-infinite edges?>but NO good evidence of infinities, e.g. no infinitely dense or hot things. What about the density of a black hole?Regardless, as I already said, claiming the absence of specific infinite things does not respond to the fact that indignities are used.>Conversely, axiom systems involving infinities have dreadful theoretical issues like uncomputability/undecideability, counterintuitive results like nondenumerability, Banach-Tarski.So what?> I'd say finite theories are backed up by more evidence and are nicer in many ways, so they should be preferred.When Wildberger does all physics without infinity then you can claim it has more evidence, until then, it doesn't.>E.g. very large numbers instead of infinities or a truncated sum instead of an infinite one.That's what a finite approximation is, I'm asking what you're approximating.
 >> Anonymous Sun Dec 9 23:40:56 2018 No.10203847 >>10203778>So are numbers. Are those real?Yes, numbers are objectively and eternally real and exist in the ideal realm
 >> Anonymous Sun Dec 9 23:41:25 2018 No.10203849 >>10203778>So are numbers. Are those real?They are idealizations that can be used to describe or model reality. We're arguing about whether infinite models/descriptions make sense mathematically and can be used to describe reality.>Mathematical machinery used to construct theories are just that, and to say that their usage implies their reality is a philosophical step too far. This doesn't respond to the argument though. Are any descriptions/models real? We can only describe what's real with them. The argument is about whether infinity can be used to do that, not whether infinity is real, whatever that means.
 >> Anonymous Sun Dec 9 23:47:14 2018 No.10203857 >>10203837>t. brainlet
 >> Anonymous Sun Dec 9 23:50:48 2018 No.10203865 >>10203837> I was responding to the claim that nonfinite mathematics does not correspond to reality, so saying that some specific thing is not "visible" is irrelevant of you admit that physics uses infinity in many ways.We do not know whether it uses infinities as it does not reveal them directly, but only indirectly in the sense that our models using them are accurate.> If they are approximations then by definition they don't fit "just as well."They fit just as well within the resolution of our measurements.>What about quantum graphs with infinite or semi-infinite edges?Can be approximated.>What about the density of a black hole?No conclusive evidence here.>So what?Some of our results might be wrong because of it. I'm not claiming that much is at stake, though, as most can be reformulated. Probably just the more exotic stuff.>When Wildberger does all physics without infinity then you can claim it has more evidence, until then, it doesn't.How do you define all of physics? We already know that all relevant calculus and algebra can re reformulated. Most of it can be left unchanged.>That's what a finite approximation is, I'm asking what you're approximating.The infinities and limits that people use to build models and make derivations.
 >> Anonymous Mon Dec 10 00:22:39 2018 No.10203919 >>10203865>We do not know whether it uses infinities as it does not reveal them directly, but only indirectly in the sense that our models using them are accurate.It uses infinities, and produces actual infinite results like the density of a black hole. We can only know things empirically by accurate correspondence to models, so you're not really making any valid distinctions.>They fit just as well within the resolution of our measurements.I'm talking about mathematically derived theories, such as irrational constants.>Can be approximated.By approximating you are admitting that finite values are not the true values.>No conclusive evidence here.Sure, if you consider relativity non-conclusive.>Some of our results might be wrong because of it. I'm not claiming that much is at stake, though, as most can be reformulated. Probably just the more exotic stuff.So basically all you have is, it might be wrong, or it's not conclusively proven, which is not a valid response to scientific facts.>How do you define all of physics? We already know that all relevant calculus and algebra can re reformulated. Most of it can be left unchanged.Incorrect, calculus hasn't been replicated with finitist axioms.>The infinities and limits that people use to build models and make derivations.So you agree that these models are more accurate since you are only approximating them with finitist math.
 >> Anonymous Mon Dec 10 01:23:01 2018 No.10204015 Reminder that the notion of finite sets is defined in terms of infinite sets, and the definitions of Dedekind-finite, Tarski-finite, Kurwatowski-finite and other definitions of finite sets that don't use the notion of infinity are equivalent to the usual definition of finite sets only in presence of AC, which is less intuitive assertion than the axiom of infinity
 >> Anonymous Mon Dec 10 01:28:42 2018 No.10204025 >>10201797You haven't proven that x+1 exist and you can't prove that it exists without axiom of infinity, so your argument boils down to "infinity exists because we said it exist".God, brainlets of /sci/ defending infinity are even dumber than all the finitists here. It's just like with flat-earthers, they're trolling by making silly claims, you act like you're smarter than them and try to prove them wrong, but the only thing you show is your incompetence
 >> Anonymous Mon Dec 10 01:35:39 2018 No.10204040 I don't like finitism (which is a valid theory and haven't been shown to contain contradictions, contrary to what most brainlets here think) because it's just CS in disguise. Just read any paper by a finitist, all they say is "Turing machine something something, computers something something, machine can't do that in finite time, therefore that's wrong, I can't write a python program that effectively constructs object under consideration, therefore the object doesn't exist".And as such finitism and intuitionism are branches of CS, not maths, and therefore it doesn't belong to /sci/, because CS is neither science or maths.
 >> Anonymous Mon Dec 10 01:37:54 2018 No.10204046 >>10200056Why are sequential arguments sufficient to prove infinities (E.g. there are infinite primes) but insufficient to prove infinitesimals?
 >> Anonymous Mon Dec 10 01:38:24 2018 No.10204047 >>10200133Unlike ur mom
 >> Anonymous Mon Dec 10 01:38:55 2018 No.10204049 >>10200167Fuck off back to the philosophy department, Aquinas.
 >> Anonymous Mon Dec 10 01:49:24 2018 No.10204060 >>10201797The fact that there are infinitely many numbers is not a contradiction in finitist theories, it just shows there are no infinite sets. Similarly, in ZFC (we use choice here to show that all sets can be given a group structure) there is no set containing all groups, and yet there do exist groups in ZFC, even though there is no container big enough to contain them all
 >> Anonymous Mon Dec 10 02:12:42 2018 No.10204089 >>10200056The answer is to treat infinity much in the same way we treat the class of all sets. This clearly isn't a set as anyone can point out, but then we just allow it to be a thing to encapsulate the broad notion of a set. This applies to 1, 2, 3, 4, etc. being actual numbers, but we can abstract the natural numbers into an infinite collection. So far, there has been nothing illogical about calling these collections sets in the same way we call {1, 2, 3} a set, we just have to be careful to know it's infinite. If you've ever done like analysis 1 then you've seen how to treat infinite sets in very careful ways based on finite evidence. So yes, we can talk about 1, 0, 1, 0, 1, 0, .... never converging even though it's at infinity as we can formulate this into a finite statement about limits.
 >> Anonymous Mon Dec 10 02:20:01 2018 No.10204095 File: 50 KB, 488x398, Religion math.png [View same] [iqdb] [saucenao] [google] [report] >>10200056>reasoning with atheists
 >> Anonymous Mon Dec 10 04:26:33 2018 No.10204202 >>10204049>Aquinaswhy?
 >> Anonymous Mon Dec 10 04:27:21 2018 No.10204204 >>10204095who needs numbers when you can solve anything with goats and violence
 >> Anonymous Mon Dec 10 08:18:24 2018 No.10204443 >>10204040>And as such finitism and intuitionism are branches of CS, not mathsthis
 >> Anonymous Mon Dec 10 08:30:33 2018 No.10204465 >>10204025>You haven't proven that x+1 exist and you can't prove that it exists without axiom of infinityIncorrect. Why are you lying about basic constructions?
 >> Anonymous Mon Dec 10 09:00:29 2018 No.10204519 >>10204202Because you are splitting hairs between apprehension and comprehension.
 >> Anonymous Mon Dec 10 09:23:56 2018 No.10204566 >>10203919>By approximating you are admitting that finite values are not the true values.The assumption is that the quantum graph also only approximates non-finite and irrational numbers, so the true (physical) values ARE approximations. This is already acknowledged for most physical phenomena, e.g. no physical object is known to be perfectly flat or perfectly circular, instead they emerge as near perfect patterns from discrete parts.>Sure, if you consider relativity non-conclusive.There is a lot more evidence for relativity than there is for the existence of infinities in black holes. Infinities at black holes are a prediction of some, but not all, relativist models. The question of what happens at the event horizon is far less settled than the accuracy of general relativity describing other physical phenomena.>So basically all you have is, it might be wrong, or it's not conclusively proven, which is not a valid response to scientific facts.Science is the process of assigning probabilities to hypotheses. I'm assigning a higher probability to finite theories but also a non-zero probability to infinite theories based on the evidence I'm seeing. That's all.>Incorrect, calculus hasn't been replicated with finitist axioms.Not all of it, but it's close enough.
 >> Anonymous Mon Dec 10 09:28:02 2018 No.10204570 >>10200133That has been disproven time and time again, but even if it were true, mathematics is still infinite.
 >> Anonymous Mon Dec 10 09:38:44 2018 No.10204589 Why the fuck are you guys arguing about the quantum graph.I specifically stated that you can not fall back on "this universe" in a counter argument. The quantum graph or any law of physics are irrelevant. Math is not an abstracted physics.If the set of all truth values extends beyond the laws of physics, then all that proves is math is a superset to the universe and the laws of physics.If this universe is finite, but we have proven there is infinity, then this universe is a finite subset of the infinite ideal realm.Choosing to limit your study to only the math relevant to the laws of this universe in no way states that math is limited to the laws of this universe - it just means that you are choosing to artificially limited the set of math that you're looking at. All of the rest of the math still exists. It's not about "usefulness".
 >> Anonymous Mon Dec 10 09:47:21 2018 No.10204602 I think you know Banach-Tarski's sphere division "paradox". In fact, it is not a paradox, because it is valid under ZFC. It is not a paradox on the real world either, because it is exactly what Jesus did with the bread and fish.
 >> Anonymous Mon Dec 10 09:49:02 2018 No.10204607 >>10204602I guess I should have also stated in the OP to not bring religious arguments into the thread either.We are talking ONLY about mathematics and why/not it IT ALONE would be limitedAlthough yes. Banach-Tarski is not a paradox.
 >> Anonymous Mon Dec 10 10:07:16 2018 No.10204633 >>10204607But he died for our sin(s)
 >> Anonymous Mon Dec 10 18:55:03 2018 No.10205800 >>10203919Check out Gerard't Hooft's work. He started discretizing our models of quantum physics and so far he has not encountered a limitation to that approach.
 >> Anonymous Mon Dec 10 19:49:48 2018 No.10205867 >>10204602>>10204607It is a paradox, and it is also valid under ZFC. This proves that ZFC is broken.
 >> Anonymous Mon Dec 10 20:10:31 2018 No.10205900 >>10205867>It is a paradoxWhy?
 >> Anonymous Mon Dec 10 22:19:59 2018 No.10206075 >>10204095Is /sci/ platonist or formalist? Please note that I left out finitism because if you are one you don't belong here and should leave as soon as possible.
 >> Anonymous Mon Dec 10 22:28:22 2018 No.10206085 >>10206075/sci/ is not /x/, so formalist.
 >> Anonymous Mon Dec 10 22:30:26 2018 No.10206090 >>10206075platonist>>10206085no
 >> Anonymous Mon Dec 10 22:33:28 2018 No.10206097 >>10206090I see you're a fellow intellectual>>10206085Don't worry friend, eventually you will achieve enlightenment
 >> Anonymous Tue Dec 11 00:01:03 2018 No.10206210 >>10206075Platonist without a doubt. I have always been a platonist.
 >> Anonymous Tue Dec 11 00:07:45 2018 No.10206218 >>10206075neither, but far closer to Platonism than formalism
 >> Anonymous Tue Dec 11 00:19:28 2018 No.10206237 >>10206097>>10206210>>10206218>math was discovered fags
 >> Anonymous Tue Dec 11 00:20:14 2018 No.10206240 >>10206237*formulated
 >> Anonymous Tue Dec 11 08:00:27 2018 No.10206687 >>10206237math literally is discovered, not invented>>10206240nope
 >> Anonymous Tue Dec 11 08:25:20 2018 No.10206721
 >> Anonymous Tue Dec 11 08:40:56 2018 No.10206745 >>10206721Math being discovered isn't paranormal you brainlet
 >> Anonymous Tue Dec 11 08:51:06 2018 No.10206760 >>10200056if trancendental numbers exist, then there must be a threshold between numbers and trancendentals, meaning its finite. Considering the number line is an 'infinite' line, there is a hole in your argument
 >> Anonymous Tue Dec 11 08:52:58 2018 No.10206764 >>10206237> discovered AND invented fags
 >> Anonymous Tue Dec 11 09:03:12 2018 No.10206782 >>10206760this makes no sense
 >> Anonymous Tue Dec 11 16:06:15 2018 No.10207515 File: 409 KB, 650x750, satanya.png [View same] [iqdb] [saucenao] [google] [report] >>10201908I tried to treat infinity as if exists. Looks like it doesn't work? Inability to treat infinity as existing is pretty telling.Do you imply that no end means infinity exists? Sounds like if one can't explain how universe came to existence then sky jew exists.
 >> Anonymous Tue Dec 11 16:12:19 2018 No.10207528 >>10200119I don't get this shit. Infinity is so damn useful, but I know when I use it in math, I'm just using it as "really really big" or "really really many". But I know this is a really simplistic view. Redpill me fgt.
 >> Anonymous Tue Dec 11 18:27:38 2018 No.10207862   >>10200408$2\cdot\infty=\infty$Therefore infinity is evenThe light is on
 >> Anonymous Tue Dec 11 18:46:55 2018 No.10207911 >>10200171The Tao that can be told is not the eternal Tao;The name that can be named is not the eternal name.The nameless is the beginning of heaven and earth. ~ Laozi
 >> Anonymous Tue Dec 11 19:09:23 2018 No.10207983 >>10207911Where's the math though, ancient chinese ramblings are not math and repeating them doesn't make you smart.
 >> Anonymous Tue Dec 11 23:05:39 2018 No.10208680 >>10207911Wow, deep. You totally convinced me.
 >> Anonymous Tue Dec 11 23:34:14 2018 No.10208738 >>10203771A rare moment of sanity from tooker
 >> Anonymous Wed Dec 12 00:10:34 2018 No.10208798 lol fucking faggit doesnt even know about inf + a one gazillion and one>i win again
 >> Anonymous Wed Dec 12 00:14:22 2018 No.10208810 File: 1.09 MB, 1292x710, 1510922075113.png [View same] [iqdb] [saucenao] [google] [report] infinity is just a placeholder for the statement:>i can just keep going on for fucking everit doesnt exist, but the outcomes gained from pretending it does makes calculations easier.>unless you are a platonist, in which case it must exist by definition, but thats just a religious belief.
 >> Anonymous Wed Dec 12 10:07:05 2018 No.10209728 >>10208810Except, of course, it does exist objectively, it has been proven, and implying it's a "religious belief" is implying that it does not have a definitive true/false value and thus must be "believed in" which is wrong. It does have a truth value, it is true, and thus it is not something to be believed in.
 >> Anonymous Wed Dec 12 10:14:22 2018 No.10209738 >>10207515lmao you're an absolute idiot
 >> Anonymous Wed Dec 12 13:00:53 2018 No.10210101 >>10203771Based
 >> Anonymous Wed Dec 12 13:06:14 2018 No.10210115 >>10206237>>10206764We invent the axioms and discover the theorems.
 >> Anonymous Thu Dec 13 01:31:08 2018 No.10211476 >>10209728nigga infinity is a concept, not a real number. it doesnt exist, but you can get big enought that the difference between results doesnt matter for any paticular scenario. surely you know the analytical definition of a limit right?
 >> Anonymous Thu Dec 13 01:51:05 2018 No.10211500 >>10200056finitism was for brainlets, true, but mathfags reject this fact since it implies hilbert was a brainlet
 >> Anonymous Thu Dec 13 07:13:58 2018 No.10211922 >i know i failed high school algebra but let me tell you the truth about infinity
 >> Anonymous Thu Dec 13 11:59:41 2018 No.10212213 >>10210115That's formalism.
 >> Anonymous Thu Dec 13 12:29:00 2018 No.10212266 >>10209728>i can prove that a number which does not exist does in fact exist.imagine being this gay
 >> Anonymous Thu Dec 13 12:39:31 2018 No.10212287 >>10212266infinity isn't a number and it does exist
 >> Anonymous Thu Dec 13 16:16:04 2018 No.10212853 >>10209728Religious beliefs have proofs. You continue to prove that mathematicians are utterly uneducated.
 >> Anonymous Thu Dec 13 16:21:40 2018 No.10212867 >>10210115Discovery of behavior of imaginary objects isn't real discovery, because it's at the mercy of imagination.
 >> Anonymous Thu Dec 13 16:37:25 2018 No.10212904 >>10200056infinity means infinite processes. you never use infinity it would require infinite time and resources you always approximate.sad but true
 >> Anonymous Thu Dec 13 16:54:12 2018 No.10212959 >>10211476>>10212266axiom of infinity>>10212853shut up
 >> Anonymous Thu Dec 13 21:27:52 2018 No.10213536 >>10212959did you really just use an axiom to counter me?an axiom is an assumption of truth, not a proof. wtf /sci/ i thought you werent retards....at least smarter than me...
 >> Anonymous Thu Dec 13 21:32:39 2018 No.10213547 >>10212287if it isnt a number then why can it be used in place of a number, like in a function for instance.?last i heard only numbers are valid domains of mathematical functions. inf is literally a placeholder statement for "i cba to carry on going up the numberline so fuk off"
 >> Anonymous Thu Dec 13 21:34:44 2018 No.10213551 and i will prove my statement without a doubt. keep counting up until you cba to count anymore, then just say "yeah whatever thats infinity i guess"there you go.
 >> Anonymous Thu Dec 13 21:59:23 2018 No.10213601 >>10213536so you want me to use something other than ZFC to talk math? doesnt that make you the retard?
 >> Anonymous Thu Dec 13 22:02:01 2018 No.10213607 >>10200056Godel bro. If we lived in a closed set math wouldn't be flawed and we would be able to account for every variable life throws at us. We would be able to account for everything inside a finite box.
 >> Anonymous Thu Dec 13 22:07:33 2018 No.10213616 >>10213547>carry on going up the numberlineall of those are just numbers,none of those are "larger than all numbers", which is the definition of infinity
 >> Anonymous Thu Dec 13 22:37:29 2018 No.10213688 >>10201785>So if infinity existed then it wouldn’t be infinite. Thats why it doesn’t exist.If infinity was reachable by finite expressions, then it wouldn’t be infinite. It exists, it just cannot be reached by finite expressions.
 >> Anonymous Thu Dec 13 22:37:57 2018 No.10213691 >>10204040This. Also intuitionism is the worst philosophy of mathematics
 >> Anonymous Thu Dec 13 22:38:49 2018 No.10213694 >>10203771Hes got a point.
 >> Anonymous Thu Dec 13 22:38:59 2018 No.10213696 >>10206721lol
 >> Anonymous Thu Dec 13 23:45:00 2018 No.10213901 >>10213601no. the axiom of choice is the entire point of why you are wrong. the choice gives you the emergent mathematical properties. its the difference between saying god is an angel vs god is a demon. both are unfounded and religious beliefs with no actual way to prove them. like ive been saying. the whole reason infinity is used is because we need a compact way to exhaust counting procedures. so instead of being 100% correct to a bajillion decimal places we just get a neat number. it does not imply any real existing entity other than its definition which has been ordained by mathematics to be assumed true.the entire thing is circular and you can not escape this.i completely agree with you though. mathematics is a wayyyyy better/prettier story when you introduce the infinite concept.
 >> Anonymous Thu Dec 13 23:52:58 2018 No.10213926 File: 74 KB, 248x247, 1508730196951.png [View same] [iqdb] [saucenao] [google] [report] >>10213616ok ill try to use this to arrive at a contradiction.>assume inf > all N>take some P = inf + 1a)>inf + 1 = inf>1 = 0or b)>inf +1 > inf>therefore inf is not the largest numberor c)>inf is a number larger than all other numbers>inf is a number>numbers always follow the laws of addition>you cant add anything to inf>counting rules are broken>contradiction
 >> Anonymous Fri Dec 14 00:32:53 2018 No.10214024 >>10213926>>inf + 1 = inf>>1 = 0Are you retarded?
 >> Anonymous Fri Dec 14 00:38:36 2018 No.10214047 >>10213926>nf is not the largest numberinf isn't a number, mr. Slow in understanding
 >> Anonymous Fri Dec 14 03:08:03 2018 No.10214154 >>10214024>>10214047>what is a proof by contradiction
 >> Anonymous Fri Dec 14 03:10:38 2018 No.10214157 >>10214024>>10214047are you a mathematician? because honestly you seem like the brainlet here. no substance to your criticism at all. i actually did math, or at least something resembling a logical method.
 >> Anonymous Fri Dec 14 03:13:07 2018 No.10214162 File: 81 KB, 349x466, 188882_tmb_481106116_10374027_10152343805031840_3218959420745653967_n.jpg [View same] [iqdb] [saucenao] [google] [report] >>10214047so inf is larger than any number, but also isnt a number, but also can be used as a number, and also exists, but not as a number, but something else.....comeon bro, youre a fucking asshole and have fully activated my almonds.
 >> Anonymous Fri Dec 14 04:57:02 2018 No.10214270 >>10214162>but something elseyup, it's an unbounded quantity
 >> Anonymous Fri Dec 14 05:01:26 2018 No.10214275 >>10214162>can be used as a number,sometimes it works like a number(**), sometimes it doesn't(***) - it isn't a number(**) 1/inf = 0 (***) 0*inf undefined
 >> Anonymous Fri Dec 14 05:13:34 2018 No.10214287 >>10214275massive abuse of notation there
 >> Anonymous Fri Dec 14 05:23:08 2018 No.10214297 >>10214287>i have no argumentW|A has no problem with it
 >> Anonymous Fri Dec 14 12:28:22 2018 No.10214864 >>10200133>discreteso then why is it finite, retard
 >> Anonymous Fri Dec 14 12:56:13 2018 No.10214910 >>10200056what is infinity made of?
 >> Anonymous Fri Dec 14 13:07:38 2018 No.10214920 >>10212959>axiom of infinityAhahaha, theology has to do the same, proofs were shat on, so they declared existence of god an axiom. You can as well say credo quia absurdum.
 >> Anonymous Fri Dec 14 13:30:47 2018 No.10214955 >>10214920this, axiomatic logic is just pulling things out of your ass, the best logic is circular logic because it stands on its own
 >> Anonymous Fri Dec 14 14:19:21 2018 No.10215066 >>10213547>last i heard only numbers are valid domains of mathematical functionsDumbest statement in this thread.>>10214275>1/inf=0I stand corrected. Everyone in this thread is an idiot. Infinity doesn't exist, the "ideal realm" doesn't exist. We have a list of statements that we declare to have property T, a way to combine those statements to form new ones and a list of rules we declare to conserve property T, then we use those rules to find out if combinations of the original statements also have the property T. Finally, we just say having property T means being true. Literally kill yourself if you see math any other way.
 >> Anonymous Fri Dec 14 14:31:36 2018 No.10215092 >>10215066numbers don't exist either
 >> Anonymous Fri Dec 14 19:49:11 2018 No.10215927 >>10200133>discrete things have to be finiteok
 >> Anonymous Fri Dec 14 20:03:26 2018 No.10215960 >>10200232the empty set is a thing. for example, it's a set with various properties, one of those being that it contains no elements.
 >> Anonymous Fri Dec 14 20:05:12 2018 No.10215962 infinity might not exist in reality, but it's fine as a mathematical formalism. there's nothing inconsistent about it.
 >> Anonymous Fri Dec 14 21:47:35 2018 No.10216147 >>10214920>t. seething middle-schooler
 >> Anonymous Fri Dec 14 23:05:31 2018 No.10216234 >>10214157>i actually did mathYou're applying the cancelation rule to an object that doesn't satisfy it. Again, are you retarded? Have you ever done real, rigorous math in your life?
 >> Anonymous Fri Dec 14 23:12:31 2018 No.10216246 >>10200133fuck off. discrete =/ finiteGo back to your undergrad studies.
 >> Anonymous Sat Dec 15 03:30:03 2018 No.10216552 >>10214275>>10213926The inf used in this way isn't "really" infinity. It's an extra element added to the set with some extra algebraic properties. In some contexts one will even add values like $\pm\infty$ and $\mp\infty$.>>10214162This is pretty standard stuff. You do similar stuff when you extend the reals as the hyperreals.
 >> Anonymous Sat Dec 15 03:45:49 2018 No.10216574 >>10215962Formalism exists, but formalism isn't infinity.
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