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/sci/ - Science & Math

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10998045 No.10998045 [Reply] [Original]

In the end, was Wildberger right?

>> No.10998067

>>10998045
Well, Wildberger is right in the sense that he is not wrong. Any formal construction of the reals eventually leads to there being weird statements that can't even be decided, like the continuum hypothesis. But it is clear to anyone that these weird quirks have nothing to do with reality. It just what happens when you add too much cocaine to your mathematics.

In the end, Wildberger is right. You CAN do everything from the finitist perspective. But my opinion as an analyst is that going for the real approach is basically a heuristic. The reals are a set where you can literally do anything. Who knew so many things would exist just by saying that all sets have a supremum. After the deep theory finds something that seems useful, it then goes into a long pipeline where it goes from pure mathematician to applied mathematician to physicist to engineer.

Can you imagine how much time it would take to make any discoveries if we had to abide by true finitist logic? Imagine if Fourier had thought about his series but discarded it because finitist technology could not express. That's not what mathematicians do. Mathematicians say FUCK IT, prove theorems with no logical basis, and then let the fuckers alive 100 years after us figure it out.

>> No.10998203

>>10998045
Yes.

>> No.10998213

>>10998045
I dont fully understand, the universe itself is infinite so why would infinite mathematics be "not true"?

>> No.10998240

>>10998067
>You CAN do everything from the finitist perspective.

not calculus

>> No.10998245

>>10998045
>end

>> No.10998248

>>10998045
I study combinatorics of infinite structures, ama.

>> No.10998253

>>10998240
Yes, you can. Wildberger has done so multiple times. The only problem is that you need to keep track of an increasing number of nuances that all just go away if you accept that R exists. But Wildberger has a complete theory of integral calculus, and differential calculus is developed as the anti-integral.

>> No.10998258

>>10998240
Wildberger actually has a series of videos of videos called algebraic calculus where he's trying to develop calculus doing exactly that.

>> No.10998260

>>10998253
no you cannot.

>>10998258
he has a video about a proof that uses the fact that numbers over a certain size can't exist and uses that to show that his theorem is correct because you only have to verify a finite number of cases

the dude is a crackpot.

>> No.10998278

>>10998260
>no you cannot.

Yes, you can. To give you a taste of Wildbergian mathematics, he argues that many things are not actually numbers. Instead, he focuses completely on the symbolic and algebraic. So after the appropriate definitions, [math] \int_0^1 \frac{1}{\sqrt{x(1-x)}} [/math] is nothing but a symbolic object. We say that there exists a field such that all of these objects have a unique value, but for Wildberger, this doesn't exist. But the object itself does exist, as we can define it algebraically. In fact, Wildberger goes on to define
[eqn] \pi = \int_0^1 \frac{1}{\sqrt{x(1-x)}} [/eqn]

So pi is just the shorthand for this object. And then, as you can imagine, you can start assigning "values" to all pi-having integrals. For example, the Gaussian integral can be solved by finding this definition of [math] \pi [/math] inside of it, etc.

Wildberger then accepts that you may have a separate theory of approximation where you can claim [math] \pi \approx 3.14 [/math], but this theory must never be based on the supposedly misguided idea that pi itself is a real thing. A pi is a symbolic object that essentially defines itself, and we may just approximate an ugly version of it for our applications.

>> No.10998300

>>10998278

>using integrals

can't do calculus without real numbers

>using pi

pi isn't real because you can't write down a representation of it. that's the same thing he says for root(2).

>> No.10998301

>>10998067
>the real approach is basically [just] a heuristic
Wildberger just wants pure mathematicians to admit what you just said.
>>10998240
>not calculus
You can. R-baby BTFOed.

>> No.10998304

>>10998301
haha i'm not surprised that people like wildberger exist, but i am surprised that people believe him and the dumb shit he says.

are you american? and in undergrad?

>> No.10998308

>>10998045
I know I’m not the smartest guy on the planet, but I just don’t see how people can honestly accept mathematics based on continuity, infinity, etc. There’s always a voice lingering in the back of my mind, saying, “this doesn’t really make sense.” It really does require faith to believe in all this stuff, especially the axiom of infinite sets. It simply isn’t logical to deduce that because we can count things in the real world, that there must be infinite numbers, or that, since we cannot perceive the discreteness of space, that continuity is a valid concept that we can work with and understand. I wish there were more mathematicians like Wildberger and that his ideas were taken more seriously so that an honest discussion could take place. But most people tend to think that humans surely could not have been erring for centuries. No! All of our mathematics is completely fine and can only go forward, they think. Infinitism is a religion, and its greatest method of survival is indoctrination.

>> No.10998320

>>10998278
>[integral] is nothing but a symbolic object
Numbers are nothing but symbolic objects. What's the point?

>> No.10998323

>>10998320
Could you please point to the object this "infinity" symbol refers to?

>> No.10998326

>>10998278
I actually like this idea...

>> No.10998328

>>10998308
I don't understand this, never at any point in my life has the concept of infinity or any of it's properties "not made sense" to me. It's very intuitive and saying it doesn't exist seems far more like faith to me.

>> No.10998341

>>10998328
On what basis do you believe that infinity DOES exist? Because to me, it seems like the product of human ignorance. We know there’s a lot that we don’t know, and we don’t know it’s finite value, so we just pretend there’s infinite things beyond us. No one fully understands infinity, and yet we trust in it to do mathematics. It’s absurd.

>> No.10998352

>>10998308

Throughout history there has been a tendency for people to revert to dogma. Academic are no exception. Many people in the sciences fall into the intellectual dishonesty trap, without even being aware of their own hypocrisy. For example take these posts >>10998304
>>10998260
The same sort of guy would have mocked Charles Darwin, or called Issac Newton a "crank".

>> No.10998357

>>10998323
It depends on the process, but here is one of the "objects" infinity refers to.
"For a given function f(x), we say f(x) as x goes to infinity is equal to the limit L if for any value ε>0, there is a number N>0 such that |f(N)-L |<ε"

>> No.10998369

>>10998357
>asks for an object
>gives an epsilon delta verification for a limit
What object, not limit, does this "infinity" symbol refer to.

>> No.10998380

>>10998369
Like I said, infinity can refer to multiple things depending on context. In this context, and in the context of evaluating an improper integral with "infinity" as pne of the bounds, "infinity" refers to the process of taking the limit to infinity. Processes are a kind of object.

>> No.10998393

>>10998341
>On what basis do you believe that infinity DOES exist?

Because I can think of it

>> No.10998396

There are different types of cranks. Wildberger is the necessary kind I think. You need that kind to reframe paradigms so you dont go down the rabbit hole of your own anus.

>> No.10998397

>>10998278
This looks like a more complicated way of conjuring up the real numbers

>> No.10998398

Assuming the existence of curves is a problem. Instead of believing that there exist lines that only become straight at a point, why not graph using only the integers, and scale graphs in order to see the general shape of the graph? For example, f(x) = x^2 will look too linear if you just look at x values from 1 to 10, but if you zoom out, and include values 1 to 1,000, we see the pattern more clearly. This is how graphing apps and websites work, anyway. From this it follows that we can find the exact area under a “curve” by simply adding up all the trapezoids formed by the graph.

>> No.10998405

>>10998301
No mathematician holds any opinion to the contrary. If one wishes to use or not use the axiom of infinity and choice etc is a matter of philosophy. It just so happens most mathematicians want to use those axioms because you can say more stuff

>> No.10998406

>>10998398
>Assuming the existence of curves is a problem.
Not really. Curves exist in nature. Scientists and engineers deal with curvature regularly. Just because brainlet mathematicians throw their arms in the air in confusion, does not make them problematic.

>> No.10998410

>>10998341
The universe is infinite in cardinality. The big bang was a local phenomenon, there is an infinite amount of big bangs happening everywhere all the time in all directions. It has no beginning and no end.

>> No.10998412

>>10998410
>The universe is infinite in cardinality
Source: your ass

>> No.10998413

>>10998323
>Could you please point to the object this "infinity" symbol refers to?
You can't point to "the object" the "3" symbol refers to, so that's a retarded argument.
The ENTIRE point of mathematics is abstraction. If you think you need to go back and connect every number to a real world object then you're completely missing that point. Numbers are anonymous. They have no inherent connection to the physical world and can be applied or not applied to whatever you want.

>> No.10998417

>>10998412
It's trivial, people just deny it because they don't like what it implies, but it requires far fewer assumptions and it jives with all known physics and mathematics far more easily than saying the universe is finite.

>> No.10998436

>>10998045
I think that the issue with infinities comes from the fact that infinite room for expansion - infinite degrees of freedom, do exist, however it is physically impossible to ever fill them up within this universe. The definitions should be more accurate to take this into account, like not implying that sets have elements but rather degrees of freedom, "slots" if you will, that you can fill up with elements which can obviously not be infinite unless they're another set on their own, like the irrationals as an example. This entire argument about infinities ultimately boils down to what is truly accepted as an element and does mashing two sets together make one of them be the element of the other, as is the case of [math]\pi \in \mathbb{R}[/math] which should not be true. In other words, "[math]\pi \in \mathbb{R}[/math]" should translate into "the degrees of freedom of [math]\pi[/math] within the degrees of freedom of the reals", neither of which form a distinct element in any other set but can exist as potential freedom within it.

>> No.10998439

>>10998406
We could just easily find approximations by using integer functions and up-scaling the graph arbitrarily. We can use the same method to find numbers approximating sqrt(2) by evaluating sqrt(200), sqrt(20,000), and so on.

>> No.10998443

>>10998417
>it requires far fewer assumptions
>it jives with all known physics and mathematics far more easily than saying the universe is finite
What the fuck? No. There is no legitimate reason to assume based on no evidence that there are infinite alternate universes.
How are you managing to make an even *MORE* insane sounding argument when your opponent is Wildberger finitist autism? Come on now.

>> No.10998444

Unrelated question: How many math professors would you guess browse /sci/?

>> No.10998448

>>10998300
>can’t do calculus without real numbers
So what just use differences instead of differentials

>> No.10998449

>>10998439
Sure, whatever. Doesn't mean that curvature doesn't exist in nature as something that we must reckon with. It obviously exists.
By the way, when in comes to actually applying mathematics, curved segments DO have a length, and there does exist a definite area beneath a curved segment. However you deal with it is your choice. Putting your fingers in your ears and crying that this isn't rigorous enough is beyond irritating.

>> No.10998480

>>10998449
For curves to have an exact area, there must be infinite intervals with length 0. But then each interval would have no area at all. This is fantasyland mathematics

>> No.10998499

>>10998480
>For curves to have an exact area, there must be infinite intervals with length 0.
Proof?

>> No.10998509

>>10998499
If there were finite intervals, then you each interval would be a trapezoid, and therefore would not be an exact area. So there must be infinite intervals and each interval cannot be finite in width, or there couldn’t be infinite intervals. So you must have a line for each point on the curve, and modern mathematics tells us that the sum of the areas of those lines is a non-zero number. Ridiculous.

>> No.10998516

>>10998509
>Ridiculous
And yet it is unimaginably powerful for applications. What gives?

>> No.10998540

>>10998516
nice that you conceded that it doesn’t make sense. Good night

>> No.10998552

>>10998540
I think it makes sense. How do you reconcile its extreme utility with it being "rediculous"?

>> No.10998614

Wildberger is definitely a crank when it comes to his objections to ZFC. He claims that the set theory axioms are really complicated and unintuitive, and when I saw them formally written out in logical symbols, I believed him. But then I actually took the time to read about the axioms and watch videos of mathematicians explaining them and why they were chosen, and I realized Wildberger is full of shit. He never actually attacks the axioms themselves or the logic they are built on.

>> No.10998616

>>10998614
How is the existence of an infinite set logical

>> No.10998630

>>10998045
No, you also get any job you want $300k starting

>> No.10998634

>>10998614
I should have added that the axiom about the infinite set is the only one that Wildberger actually devotes any time to attacking.
>>10998616
But anyways, how is an infinite set not logical? There are a countless amount of numbers, and for any number you list, you can always go one higher. Wildberger’s finitism is really only “logical” for practical concerns.

>> No.10998671

>>10998614
I wouldn't call him a crank, but considering that ultrafinitism is as old as math, he seems to never really fine tune the proper philosophical arguments and just appeals to intuition and "logic". It's a really complicated debate, but if he wants to throw something as useful as reall analysis to the toilet, he should clarify his arguments regarding infinity.

>> No.10998767

>>10998213
>universe is infinite
how do you even know that?

>> No.10998772

>>10998444
all of them.>>10998448

>> No.10998823

>>10998328
It's been the opposite for me. Throughout high school I constantly asked questions about infinity, I was particularly stubborn in accepting limits. Eventually I took the leap of faith to accept infinitism because you cant succeed in modern math without it. Once I accepted it as an axiom thinking about it became intuitive, but when I was younger the concept of infinity baffled me. I can still revert to the finitism perspective and argue for it, but it's just infinitely more practical at the moment to accept infinitism as an axiom (pun intended).

>> No.10998837

>>10998449

Spot on! Now go and fix that lawn mower.

>> No.10998857

>>10998406
>Curves exist in nature.
top kek

>> No.10999046

>>10998300
Brainlet post. You are retarded and I know you are undergrad or worse. Missed the entire point of the explanation.

>>10998320
You should ask Wildberger but he'd say that the problem lies that when you suppose that R exists, you introduce a bunch of weird questions. See, for example, Continuum Hypothesis. But if you just introduce say [math] \mathbb{Q}[ \pi ] [/math], no such questions arise.

>>10998326
I like it too but it has some flaws. For example, what if we didn't already know what integral to use to define pi? We'd need ungodly amounts of intuition to do any progress. Meanwhile right now we can just assume everything exist and eventually find their values.

>>10998397
No because you would never be able to get more than a countable set of new numbers.

>> No.10999165

>>10998634
>and for any number you list, you can always go one higher
This is unsupported. You’re assuming what you’re trying to prove: that for any number, there exists a number greater than it. And by your exact words, does this mean that we can only go higher if we can at first list a number? So all the numbers that are too large to list aren’t actually numbers?

>> No.10999181

>>10998240
Derivatives ~ Finite Differences
Integrals ~ Summations
Differential Equations ~ Difference Equations
etc
If anything, the general case for the discrete calculus is way more complicated because even less things have analytic formulas. Being able to discard error terms because they go to zero when you pass the limit is a very powerful tool.

>> No.10999191

>>10998323
Sure. Infinity is a shorthand for the equivalence class of sets with subsets that have the same cardinality as the natural numbers.
Likewise 7 refers to the equivalence class of all things we can count 7 instances of.
And so and so on.

>> No.10999236

>>10999046
>Continuum Hypothesis
Continuums exist in nature. It would be nice to have an abstracted set of tools that deal directly with or in a continuum. Why is Wildberger so against this?

>> No.10999257

>>10998443
I never said anything about infinite alternative universes. There is one universe, it's all here. If you were to get into a spaceship and travel in some direction for a very very very long time you'd leave this universe and continue to move in that direction into another local big bang cluster.
The universe can be thought of as R3

>> No.10999259

>>10999236
>Continuums exist in nature
Prove it

>> No.10999264

>>10998509
Literally nothing about that is unintuitive or ridiculous or nonsensical.

>> No.10999271

>>10999259
*observes a steel beam*
*observes a body of water*

>> No.10999276

>>10999236
As far as I remeber, Wild has not commented on RH. I just give CH as an example of the weird undecidable statements that pop up if you try to define the reals rigorously. Another good example non measurable sets.

>> No.10999281

>>10999271
Those images on computer screens would look continuous too, but they aren’t

>> No.10999285

>>10999276
>Another good example non measurable sets.
I thought the existence of nom-mesurable sets depended on the axiom of choice, not on the existence of infinite sets.
You can make the reals without choice.

>> No.10999287

>>10999259
Empty space itself is a continuum. There are no "pixel" in the fabric of SpaceTime and there is no argument you can make against this truth.

>> No.10999288

>>10999281
How do you propose developing the theory of elasticity or fluid mechanics without the continuum? Sounds like you hate it when scientists or engineers are able to predict nature.

>> No.10999292

>>10999287
>Empty space itself is a continuum
Proof?
>>10999288
Calculus is useful, yet at the very heart of it, it makes no sense. See >>10998509
Just because it’s useful doesn’t mean it’s true. You literally just have faith that the world is continuous.

>> No.10999300

>>10999292
>>Empty space itself is a continuum
>Proof?
lmao you're a retard
>"so you don't have proof?"
Literally all evidence shows space is continuous, it is not "little squares" or something and it's not a flaw in our tools ability to look close enough.
You just deny this because you don't like it, not because it's not true. If you want to argue that particles are discretized, you'd be wrong but there's a slightly stronger argument you could make but for the fabric of spacetime itself there is no argument or evidence that you can give at all that shows anything other than continuity.

>> No.10999305

>>10999300
yeah, I’m not seeing any proof here. I bet you think HD movies are continuous too, right?

>> No.10999309

>>10999292
>it makes no sense.
I disagree. What seems to baffle that poster is very intuitive to me.
>I have faith the world is continuous
I actually know for a fact that a solid material is not literally continuous. But with the goal of analyzing stresses and deformations, making the assumption that it is continuous is extremely useful. I think you agree up to this point.
If I am going to make the assumption that a material is continuous for practical reasons, I will need some sort of mathematical framework that deals with the continuum. This is why calculus was developed. Real analysis was developed to set these math tools on more rigorous basis. When you notice there are still unresolved issues in analysis, please do not throw the baby out with the bath water.
Whenever I hear Wildberger talk about how rational trig/calculus is more intuitive, or is a good alternative for scientists and engineers, I fucking cringe.
>>10998857
>dude what is GR
>lol what even is a spline

>> No.10999310

>>10999287
The universe is in fact discrete. As are the numerous dicks you service repeatedly with your asshole and mouth every day. The only thing continuous is your feeble-brained bitching in this thread.

>> No.10999321

>>10999305
Explain how empty space can be 'discrete' despite all evidence.
>>10999310
The universe is in fact continuous. All evidence indicates it's continuous and the only way to say it's not is to simply say "it's discrete!" when it's not. Explain how empty space can be discretized (and thus not empty) you retard.

The only way finitist EVER make their "arguments" is they say "no there is in fact a largest number, and no number can go beyond it. Why? I dont' know, you can't write it down or something. Also I don't know what the number actually is or why you can't add 1 to it".
You guys are actually not smart at all, you think you've stumbled upon some hidden truth or some grand error in logic but in reality you just aren't very smart and aren't very capable of seeing things that the majority of people are able to intuitively understand. This is not an ad hominem because it is an accurate depiction of you.

>> No.10999333

>>10999321
still no proof. Sad. Are you the same guy that thought steal beams prove that reality is continuous, and tried to use a different argument when I pointed out that images can appear continuous on screens, which we know are discrete? You probably think that because you can draw a curved line with a pen, that continuous curves actually exist. You’re basing your view of reality on an illusion

>> No.10999337

>>10999333
No I'm not the same guy that thought that steel beams are continous, I even said you could make the argument that particles are discretion (although they aren't, they exist in a probability space that is a subset of the reals and are thus continuous).
So I'll ask you again, how can empty space be discretized, which would imply it's not empty? Stop talking about screens on HD tv's or some faggot shit we're talking about physical reality here, not simulations.

>> No.10999338

>>10999337
argument that particles are discrete*

>> No.10999347

>>10999337
How can empty space be continuous? You haven’t proven anything. I never even claimed reality was discrete. But I don’t see the reasoning for it being continuous either

>> No.10999350

>>10999333
I'm the guy who bought up steel beams. You misunderstood me. Read >>10999309

>> No.10999360

>>10999347
If it's actually made up of discretized "cells' it's not empty anymore, it's an ether and not empty space. That's been disproven, so we're left with continuous empty space.
Particles are a probability cloud that is continuous, it's a subset of the reals, again not discrete.
The argument for discreteness that people make is always built off a false understanding of what the Planck length means. It doesn't imply non-continuity at all. There is no evidence of anything but continuity, and the only "argument" discrete people have is to go "no it's actually a bunch of little blocks like on a TV screen! Also there IS a gretest natural number for some reason even though I can't tell you what it is or why you can't add one to it!"
This shit is a joke, there's a reason it's not taken seriously and it's not because mathematicians and scientists are in a 'cult' or some shit. It's because it makes no sense, ignores all evidence, and is clearly motivated by some weird need for reality to be clean like stacking little blocks like an autist rather than the big gloopy random scary mess it actually is.

>> No.10999370

>>10999360
>If it's actually made up of discretized "cells' it's not empty anymore, it's an ether and not empty space. That's been disproven, so we're left with continuous empty space.
How has that been disproven? What do you think space is? Hint: it’s not nothingness.

>> No.10999372

>>10998320
and yet I can count very real natural numbers. So you're full of shit and refuse to admit you're wrong and that there is a clear distinction between things you can actually count and things you can't even write down or describe if we gave you until the heat death of the universe.

>> No.10999377

>>10999370
Vacuum fluctuations are also continuous. As are particles. Still nothing discrete about it.

>> No.10999382

>>10999370
>>10999377
Also yes, Aether has been disproven and discarded, only crackpots still talk about an "aether".

>> No.10999390

>>10998260
>>10998300
>>10998304
what does being a brainlet look like? Is your ability for abstraction so limited you can't even consider the possibility of something you haven't been taught by your elementary school teacher?

>> No.10999392

>>10999372
And yet I can calculate to e or pi or the square root of 2 to however many digits you could possibly want. You are getting hung up on the same things that the ancient greeks were able to get over.

>> No.10999395

>>10999288
yeah? Solve the Navier-Stokes equations
Oh wait you can't.
Solve the cosmological constant problem
Oh wait you can't.
Solve anything that requires regularization without party tricks.
Oh wait you can't.

>> No.10999400

>>10999395
I don't know how this has any bearing to what we are talking about

>> No.10999401

>>10999392
Define e or pi. I too can write a random string of numbers.

>> No.10999404

>>10999400
because you're a brainlet. Try to at least understand why integrals sometimes lead to infinite or vastly overestimated results compared to the value they're supposed to have in reality.

>> No.10999412

>>10999401
>pi and e is random
lol
>>10999404
No argument. Navier-stokes can always be solved numerically, btw. This is adequate.
Why do you care more about games you play with symbols on a piece of paper than reality?

>> No.10999421

>>10999412
define them or gtfo. Now that you're challenged on your foundations you're starting to panic?
https://youtu.be/lcIbCZR0HbU?t=2069
>Why do you care more about games you play with symbols on a piece of paper than reality?
because the symbols you use to compute give false results. With our best theory using real numbers, we get a result that's 120 orders of magnitudes wrong on the cosmological constant.
And as you say, computations are made numerically, ie with algorithms that terminate and that are well defined.

>> No.10999429

>>10999421
pi is the ratio of the circumference to the diameter of any circle
e is the limit of (1+1/n)^n as n goes to infinity (I already defined limits to infinity in this thread)
sqrt(2) is the ratio of the hypotenuse of any right, isosceles triangle to one of its legs.
>the symbols give false results
No? They are unreasonably effective.

>> No.10999435

>>10999412
>Navier-stokes can always be solved numerically, btw.
If existence and smoothness pf solutions are in doubt there's no guarantee that the calculations will actually converge or approach any value that actually makes sense, btw

>> No.10999449

>>10999429
>circles exist
>infinity exists
>right isosceles triangles exist

>> No.10999455

>>10999449
Circles and triangles and LIMITS to infinity are all well defined mathematical objects

>> No.10999465

>>10999449
Said no one ever

>> No.10999470

>>10999455
>a set of infinite points can exist
Sorry, I don’t buy it. I’ve never seen a real circle

>> No.10999472

>>10999470
Good thing mathematics isn't dependent on what you have seen personally.

>> No.10999527

>>10999285
But that is the thing. Pondering the reals leads up to asking about measurable sets and that is undecidable until you add more axioms.

>> No.10999627

>>10999165
Okay so then what’s the last number, if adding numbers is apparently “unsupported” now?

>> No.10999641

Until finitists explain why there is a final number and why you can't add 1 to it, they can never make the argument that finitism is "more intuitive" than infinity.

>> No.10999650

>>10999627
If I knew what the last number was, then it probably wouldn’t be the actual last number, since I could theoretically easily conceive of such a number and that number + 1. The real last number would be something so large that all numbers beyond it are irrelevant for a finite universe, and cannot be computed or even fathomed by any sentient being or computer within that universe.

>> No.10999659

>>10999650
Whether or not a sentient being or computer can "fathom" a large number has nothing to do with whether or not the number is the last one.
And the universe is infinite so I really don't understand why you all continue to say talk about a "finite universe". The physical universe we live in doesn't have a boundary or edge, you can continue to move infinitely in any direction, why do you keep talking like it has an end.

>> No.10999665

>>10999650
>The real last number would be something so large that all numbers beyond it are irrelevant for a finite universe, and cannot be computed or even fathomed by any sentient being or computer within that universe
But we could still theoretically add 1 to that number. Addition doesn’t cease to exist because of limits on computation power.

>> No.10999669

Check em

>> No.10999670

>>10999665
Exactly, why do they keep saying this shit it doesn't make sense.

>> No.10999671

>>10999650
Why are you limiting mathematics to how the physical universe behaves

>> No.10999675

>>10999641
Being able to add 1 implies that the next number already exists. You’re essentially saying that for all numbers, there exist greater numbers. In other words, you’re assuming the existence of infinite numbers. You’re bothered by the possibility that there may be a last number and that we couldn’t add anything to it, but if it’s the last number, then we would never approach a situation in which we could even conceive of that last number. You’ve taken the real world concept of adding objects and assumed that you can do the same thing with abstract numbers without end. But to simply say that there for any number N, there exists N +1, is a meaningless expression as the “+ 1” has real meaning to it.

>> No.10999683

>>10998045
>Wildberger
would anyone unironically learn math from his channel or if you use it irl/ in university will people just think you're schizo/brainlet?

>> No.10999689

>>10999675
>Being able to add 1 implies that the next number already exists.
No it doesn't, it could already exist OR it could immediately be constructed the moment you do the +1 operation on the previous number. Either way, though, you can't have a "final number" it makes no sense.
You're literally saying there's some arbitrary number that just acts differently from all the other numbers in this case for no reason just because. It makes no sense.

>> No.10999693

>>10998045
>finitism
This board is for science and math, not philtards.

>> No.10999694

>>10999675
Why is there a last number? Why are you assuming that there is something preventing us from adding onto abstract numbers without end?

>> No.10999701

>>10999694
Why are you assuming there are infinite numbers? You can’t prove it either way. Infinite numbers is only definitely valid under an infinite universe.

>> No.10999706

>>10999693
No one has ever apprehended the infinite in any way. Ignorance doesn’t imply the existence of infinity. All we know is the finite.

>> No.10999707

>>10999701
>Why are you assuming there are infinite numbers? You can’t prove it either way.
See >>10999689
>You're literally saying there's some arbitrary number that just acts differently from all the other numbers in this case for no reason just because. It makes no sense.

>Infinite numbers is only definitely valid under an infinite universe.
Why?

>> No.10999708

>>10999701
The universe is infinite so again, this isn't a counter argument. Even if the universe were not infinite, why would that somehow mean there is a "final number"?
Assign to every particle some number going up to the N amount of particles. Then we'd have a "largest number". Then just reset the sum starting from this "largest number" and we can continue to go forever with no upper bound.
EVEN IN a finite universe (which the universe isn't, the universe is infinite so it doesn't even matter) we still do not have a "final number".

>> No.10999718

>>10999429
>pi is the ratio of the circumference to the diameter of any circle
What is a circle exactly? Also how do you measure that circle's circumference?

>> No.10999720

>>10999706
We can rigorously define limits to infinity and what it means for a limit to be unbounded. We also can't comprehend the number 10^23. Is 10^23 also non existant?

>> No.10999722

>>10999683
His differential geometry lectures are pretty good.

>> No.10999728

>>10999718
The set of points that are a given radius from a center point. If you don't know what pi is, you can measure a circumference with a tape.

>> No.10999742

>>10999728
there is only a finite amount of points that are a given radius from a center point. In fact, it can even be 0. How do you measure any distance using that set of points?

>> No.10999744

>>10999720
10^23 can be measured, such as when you measure the mass of large objects, or calculate probabilities, etc. The largest number would never be applicable in any calculations in a finite universe. It could never be reached, so there wouldn’t be any problems.

>> No.10999751

>>10999744
Infinity isn't a number. Process that involve infinity can be easily defined.
>>10999742
>there are a finite number of points
I disagree. But supposing there are finite number of points, it is a trivial matter of summing the distance between each point.

>> No.10999766

>>10999751
>Infinity isn't a number
oh, that’s right, it’s an unbounded “quantity”

>> No.10999771

>>10999766
No, it isn't that either. It is shorthand for limiting processes "that go to infinity." This conversation is reminding me of people of people who get hung up on imaginary numbers because of their name.

>> No.10999780

>>10999744
THE UNIVERSE ISN'T FINITE FUCKING IDIOT why do you keep saying this?
The universe is expanding which automatically implies infinity.

>> No.10999787

There is no debate if you take a formalist approach to mathematics.

Generally, the word "exist" is so loose that there's barely any use in engaging in a conversation about it. This is true for common sense object, and even more so with mathematical entities.

>>10998067
The continuum hypothesis is not the best example of an undecidable problem - there are many statements about the natural numbers that can't be decided either.
https://en.wikipedia.org/wiki/List_of_undecidable_problems

>>10999236
>Continuums exist in nature
That's a philosphical statement.

>> No.10999791

>>10999771
>infinity is shorthand for limiting processes "that go to infinity."
lmao wtf am I reading. This is a recursive definition.
>>10999780
I never said the universe is finite. But since you claimed it isn’t, can you prove it?
>The universe is expanding which automatically implies infinity.
That doesn’t follow at all

>> No.10999799

>>10999791
>This is a recursive definition
No it isn't. Look up the precise definitions of "limits to infinity" and what it means for a limit to not converge. Hint 1: the word infinity is not invoked in the definitions. Hint 2: I've already provided these definitions ITT.
Btw, the other guy you are talking to is a straight up retard.

>> No.10999806

>>10999791
>That doesn’t follow at all
Yes it does. the fuck are you talking about?
The big bang was a local phenomenon that's expanding out into the infinite universe, there is an infinite amount of big bangs happening every second all over the place all the time. There is no "beginning" and no "end".

>> No.10999810

>>10999806
>there is an infinite amount of big bangs happening every second all over the place all the time
No proof

>> No.10999816

>>10999799
You still haven’t defined “infinity.” With limits, we could just as easily say “as x gets arbitrarily large” rather than “as x goes to infinity.” If x is going to infinity, then what is infinity?

>> No.10999817

>>10999799
>Btw, the other guy you are talking to is a straight up retard.
Smarter than you, trying to justify infinite by definition of infinite process. Fucking retard, just point out that infinity exists in physical reality and you don't need to make these arguments from definitions, which don't hold up to scrutiny because we can just define limits in a different way. You're arguing axiomatically when this isn't about axioms.
>>10999810
Our big bang is proof (okay, strong evidence). Otherwise you're arbitrarily limiting the universe and denying expansion for no reason just because you don't like infinity.

>> No.10999845

>>10999751
>But supposing there are finite number of points, it is a trivial matter of summing the distance between each point.
then pi doesn't exist, assuming a notion of distance between points even exists

>> No.10999859

>>10999671
Because mathematics explains how the physical universe behaves.

>> No.10999874

>>10999671
Because the universe cannot violate mathematics

>> No.10999875

>>10999816
That's not what a limit to infinity is. Go back to calculus 2.

>> No.10999919

I appreciate what he's trying to do, but also don't care because real numbers are cool.

>> No.11000001
File: 101 KB, 750x750, eyez.jpg [View same] [iqdb] [saucenao] [google]
11000001

Regarding constructivism, for people interested, I had recently shown e.g. how to prove the law of non-contradiction [math] \neg( P\land \neg P) [/math] constructively, which classically is equivalent to the law of excluded middle [math] \neg P\lor P) [/math]. Generally, for every classically provable statement [math] Q [/math], there's a constructive proof of a statement [math] Q' [/math] that's classically equivalent to to it. So you don't lose anything (but making the proofs harder and more algorithmic) when you do things purely constructively. And at the same time there's some nice theories (e.g. differential geometric ones) that aren't consistent classically - so you lose something going classical.
More high level, there's also a survey on axiomatizations of constructive set theory, sorted by axiom strength

https://youtu.be/Fyfvwu1dejA
https://youtu.be/HrN7orXvu9k

>> No.11000035

Brainlet here.
This is really cool, but I need some help.
I would define the universe as what exists.
Space as the distance between two or more things.
So as the light or tachyons or some shit at opposite ends of the universe move away from eachother Space is expanding. Even if that rate of expansion is increasing we can't say it will continue to do so forever. So you could say that the universe is finite, space is expanding and will at some point stop expanding and at that point space will be finite.

>> No.11000039

>>10999859
No it doesn't.
>>10999874
Mathematics are completely abstract. Math has nothing to do with the universe.

>> No.11000054

>>11000039
>Mathematics are completely abstract. Math has nothing to do with the universe.
Then why study mathematics? Why concern yourself with something if it has nothing to do with the real world?

>> No.11000062

>>11000054
>Then why study mathematics
Because it is a useful tool. It doesnt say anything about the universe on its own.

>> No.11000078

>>10998045
> they tell you an absolute truth after you defend.
If that is they case all math phd's are retards because if you haven't figured out what elements are "true" and practical of your field on your own you didn't do a phd

>> No.11000080

>>11000054
Why do music or go to a music concert?

>> No.11000105

>>11000062
>>11000080
So truth is irrelevant, and only utility is important?

>> No.11000112

>>11000105
I don't know why you reply to the application fag and me in one response

>> No.11000120

>>11000105
That's not what I said. Mathematics is nothing but a logically consistent framework that helps solve practical problems. There is nothing logically inconsistent about infinite limits.

>> No.11000163

>>10999292
The burden of proof is on you niqqa

>> No.11000178

>>11000163
For what claim?

>> No.11000186

>>11000120
sum from x=1 to inf (x) = -1/2

>> No.11000197

>>10998045
You know what? Quantum physics IS like magic at exactly one point: Quantum computing as an idea can never be falsified. Only individual models can be falsified, and they come with testable hypotheses. More generally, there's no way to prove that quantum computing isn't possible. If there were, it would directly imply a falsifiable hypothesis to test, and it would only be falsifying a single orientation in Hilbert space. You literally can't test an infinite number of hypotheses simultaneously.

>> No.11000200

>>11000186
No it isn't. And no, numberphile is not a source. [math]\sum_in_i[/math] is a divergent sum.

>> No.11000430

>>10999780
No.. it doesn't and with a finite amount of matter the expansion would have to stop eventually due to 'the big freeze' so it would stop at a finite size with a finite amount of matter.

>> No.11000471

>>10998045
Oh yeah, for sure, differential and integral calculus is never used in science BAHAHAHAHAHA fucking retard. Dynamical systems and PDEs are never used in science.
I risk taking the bait, but goddamn calling you a fucking moron is too satisfying.

>> No.11000504

>>10999780
> The universe is expanding which automatically implies infinity.
Idiotic logic.

The Cosmic Horizon has in fact a finite limit. It means every particle will eventually be isolated completely from any other particle.

>> No.11000510
File: 13 KB, 339x235, 1532979026167.jpg [View same] [iqdb] [saucenao] [google]
11000510

>>10998213
>the universe itself is infinite

>> No.11001729

>>10998352
>The same sort of guy would have mocked Charles Darwin, or called Issac Newton a "crank".
Asserting that there's a largest number DOES make you a crank.