/sci/ - Science & Math

>>10200056
>Implying that you'll find people that are nearly educated enough (ultra)finitists here

>>10200056
Infinity 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.

>>10200056
fuck off. the universe is discrete

>>10200133
The universe is a subset of mathmatical infinity.

>>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?
>>10200133
Completely irrelevant

>>10200133
>muh planck length

>>10200139
They aren't problems. OP's premise is flawed.

>>10200152
>OP's premise is flawed.
No it isn't

>>10200056
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.

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.

>>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?

>>10200161
You don't want to listen to mine or your own so I obviously am not the one you would accept satisfaction from.

>>10200167
You are mixing up 'uncountable source of x' with 'expansion to allow x -> y'

>>10200119
basically 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

>>10200167
You'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.

>>10200171
Because it's the equivalent of trying to define/conceptualise "nothing".

>>10200175
Expansion is a finite property.

>>10200187
>if you set it to X, you're already assuming it's known
Known in what way?

>>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"

>>10200197
O

>>10200213
K

>>10200202
Expansion yes, successor functions no

>>10200225
It was supposed to be the null set.
Anyway, here is nothing: {}
not hard to define or conceptualize

>>10200230
A quantity of successor functions?

>>10200232
>Anyway, here is nothing: {}
I see brackets? Brackets are something.

>>10200238
+1 until failure

>>10200056
Suppose 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)

>>10200363
>+1 until failure
wat

>>10200240
you should honestly jump off a bridge

>>10200056
I do not assume the axiom of infinity.
The burden of proof lies on you to explain why I should.

>>10200444
no ur mom

>>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 premises
you havent demonstrated a problem with infinity

>>10200452
>literally just ignoring the question and acting like youre smart for being a coward

>>10200452
No, the burden of proof is on you to show me which natural number is the largest

>>10200463
6

>>10200460
>implying questioning the assumptions behind the question is ignoring the question

>>10200056
The 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.

>>10200481
>implying theres a coherent way to question the assumption
>"theres a largest finite set of size N"
N+1gger

>>10200056
No infinity - no problems.

>>10201333
but there is an infinity (multiple, actually) so try again

>>10201694
Source: your ass.
If there's infinity, then tell me the infinith digit of pi.

>>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.

>>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.

>>10201758
>NUMBERS ARE FINITE
Yes? 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.

>>10201777
>If mathematics is supposed to be isomorphic
It 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.

>>10201785 (you)

The x be the largest positive integer
(x+1) > x
Contradiction
Therefore, there is no largest positive integer.

QED

>>10201785
You didn't tell him what the largest number is
What is the largest number?
>>10201797
This

[math]\mathscr{P}(\mathbb{C})[/math]
Now what, fags?

[math] \mathscr{P} ( \mathbb{C} ) [/math]
Now what, fags?

>>10200056

>>10200167
How is it treated like a finite thing incorrectly?

>>10200408
On, since 2^(-0) = 1. 0 is the first natural number, so the first time you switch the lamp is at t = 1.

>>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 number

if the digits had an end they would be finite
if 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

>>10201777
I 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.

>>10201932
Lmao this

>>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.

>>10201932
Nope. Even some physicists are considering this possibility, see e.g. section VII. C in this paper:

https://arxiv.org/pdf/0704.0646.pdf

The 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.

>>10200408
You 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.

>>10201859
>using \mathscr{P} instead of \wp for the powerset

>>10201751
There is none, all digits of pi correspond to a natural number.

>>10201777
Physics uses infinity, infinite numbers, limits, calculus, etc. so your assumption that only finite objects correspond to reality is empirically false.

>>10201751
>if there is no last digit of pi, then tell me the last digit of pi
This is your brain on finitism.

>>10201975
Here's what I usually use (piss poor spam detection):
https://pastebin.com/dFxfWNrB

But yeah, maybe I did pick poorly.
[math] \wp{ ( \mathbb{C} ) } [/math]

>>10200133
time

>>10201829
nah, 10201798 is larger

>>10200056
I 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.

>>10200133
So is time not finite? How exactly does Time begin and end?

>>10201982
No 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.

>>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?

>>10203721
>How does that respond to my post?
How does that respond to my post?

>Finite approximations of what?
thereof.

>>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.

>>10200167
what 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?

>>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.

>>10203745
Oh look it's another finitard reduced to shitposting after getting BTFO.

>>10203763
>t. brainlet

>>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.

>>10200056
I'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?

>>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

>>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.

>>10203778
>So are numbers. Are those real?
Yes, numbers are objectively and eternally real and exist in the ideal realm

>>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.

>>10203837
>t. brainlet

>>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.

>>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.

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

>>10201797
You 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

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.

>>10200056
Why are sequential arguments sufficient to prove infinities (E.g. there are infinite primes) but insufficient to prove infinitesimals?

>>10200133
Unlike ur mom

>>10200167
Fuck off back to the philosophy department, Aquinas.

>>10201797
The 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

>>10200056
The 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.

>>10200056
>reasoning with atheists

>>10204049
>Aquinas
why?

>>10204095
who needs numbers when you can solve anything with goats and violence

>>10204040
>And as such finitism and intuitionism are branches of CS, not maths
this

>>10204025
>You haven't proven that x+1 exist and you can't prove that it exists without axiom of infinity
Incorrect. Why are you lying about basic constructions?

>>10204202
Because you are splitting hairs between apprehension and comprehension.

>>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.

>>10200133
That has been disproven time and time again, but even if it were true, mathematics is still infinite.

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".

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.

>>10204602
I 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 limited
Although yes. Banach-Tarski is not a paradox.

>>10204607
But he died for our sin(s)

>>10203919
Check 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.

>>10204602
>>10204607
It is a paradox, and it is also valid under ZFC. This proves that ZFC is broken.

>>10205867
>It is a paradox
Why?

>>10204095
Is /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.

>>10206075
/sci/ is not /x/, so formalist.

>>10206075
platonist
>>10206085
no

>>10206090
I see you're a fellow intellectual

>>10206085
Don't worry friend, eventually you will achieve enlightenment

>>10206075
Platonist without a doubt. I have always been a platonist.

>>10206075
neither, but far closer to Platonism than formalism

>>10206097
>>10206210
>>10206218
>math was discovered fags

>>10206237
*formulated

>>10206237
math literally is discovered, not invented
>>10206240
nope

>>10206090
>>10206097
>>10206210
>>10206218
>>10206687
>>>/x/

>>10206721
Math being discovered isn't paranormal you brainlet

>>10200056
if 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

>>10206237
> discovered AND invented fags

>>10206760
this makes no sense

>>10201908
I 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.

>>10200119
I 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.

>>10200408
[math]2\cdot\infty=\infty[/math]
Therefore infinity is even
The light is on

>>10200171
The 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

>>10207911
Where's the math though, ancient chinese ramblings are not math and repeating them doesn't make you smart.

>>10207911
Wow, deep. You totally convinced me.

>>10203771
A rare moment of sanity from tooker

lol fucking faggit doesnt even know about inf + a one gazillion and one

>i win again

infinity is just a placeholder for the statement:

>i can just keep going on for fucking ever

it 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.

>>10208810
Except, 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.

>>10207515
lmao you're an absolute idiot

>>10203771
Based

>>10206237
>>10206764
We invent the axioms and discover the theorems.

>>10209728
nigga 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?

>>10200056
finitism was for brainlets, true, but mathfags reject this fact since it implies hilbert was a brainlet

>i know i failed high school algebra but let me tell you the truth about infinity

>>10210115
That's formalism.

>>10209728
>i can prove that a number which does not exist does in fact exist.

imagine being this gay

>>10212266
infinity isn't a number and it does exist

>>10209728
Religious beliefs have proofs. You continue to prove that mathematicians are utterly uneducated.

>>10210115
Discovery of behavior of imaginary objects isn't real discovery, because it's at the mercy of imagination.

>>10200056
infinity means infinite processes. you never use infinity it would require infinite time and resources you always approximate.
sad but true

>>10211476
>>10212266
axiom of infinity

>>10212853
shut up

>>10212959
did 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...

>>10212287
if 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"

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.

>>10213536
so you want me to use something other than ZFC to talk math? doesnt that make you the retard?

>>10200056
Godel 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.

>>10213547
>carry on going up the numberline
all of those are just numbers,
none of those are "larger than all numbers", which is the definition of infinity

>>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.

>>10204040
This. Also intuitionism is the worst philosophy of mathematics

>>10203771
Hes got a point.

>>10206721
lol

>>10213601
no. 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.

>>10213616
ok ill try to use this to arrive at a contradiction.
>assume inf > all N
>take some P = inf + 1
a)
>inf + 1 = inf
>1 = 0

or b)
>inf +1 > inf
>therefore inf is not the largest number

or 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

>>10213926
>>inf + 1 = inf
>>1 = 0
Are you retarded?

>>10213926
>nf is not the largest number
inf isn't a number, mr. Slow in understanding

>>10214024
>>10214047
>what is a proof by contradiction

>>10214024
>>10214047
are 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.

>>10214047
so 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.

>>10214162
>but something else
yup, it's an unbounded quantity

>>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

>>10214275
massive abuse of notation there

>>10214287
>i have no argument

W|A has no problem with it

>>10200133
>discrete
so then why is it finite, retard

>>10200056
what is infinity made of?

>>10212959
>axiom of infinity
Ahahaha, 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.

>>10214920
this, axiomatic logic is just pulling things out of your ass, the best logic is circular logic because it stands on its own

>>10213547
>last i heard only numbers are valid domains of mathematical functions
Dumbest statement in this thread.
>>10214275
>1/inf=0
I 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.

>>10215066
numbers don't exist either

>>10200133
>discrete things have to be finite
ok

>>10200232
the empty set is a thing. for example, it's a set with various properties, one of those being that it contains no elements.

infinity might not exist in reality, but it's fine as a mathematical formalism. there's nothing inconsistent about it.

>>10214920
>t. seething middle-schooler

>>10214157
>i actually did math
You'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?

>>10200133
fuck off. discrete =/ finite

Go back to your undergrad studies.

>>10214275
>>10213926
The 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 [math]\pm\infty[/math] and [math]\mp\infty[/math].

>>10214162
This is pretty standard stuff. You do similar stuff when you extend the reals as the hyperreals.

>>10215962
Formalism exists, but formalism isn't infinity.