Feels over Reals (Literally)

>>8889598
this guy looks like a clit with a wig

is he for real? is this a joke? what kind of new mathematical concept is defined in a fucking youtube video? this is laughable, it's a piggot oinkery

>>8889598
Algebraic calculus? I'm unfamiliar with the term. What is it?

This man is my god
that pure smugness as he unravels our notation of maths showing its true glory, as he BTFO of the old """""""mathematicians""""""""" lost in their own ways of formalism, simply because they couldn't see what he can.
At last i truly understand

>>8889605
>is he for real?
yes
>is this a joke?
yes

He doesn't understand metamathematics and his youtube videos on set theory are hilarious... but apparently he is a professor and got stuff published before going nuts.

>>8889605
>is he for real?

No, he is for rational.

>>8889635
Underrated post

>>8889625
>he is a professor
In Australia because they needed a diversity hire and the Aussies were too drunk to function.

>>8889663
Wildberger is white though

>>8889598
I would be interested to know how a person would turn out if they learned the foundations of math the way Wildberger does it.

>>8889663
do fucking white american males count as "diversity" in Australia? If so then I need to move there

>>8889692
Well, maybe the immigration into australia is pretty low as they are literally an island. Thus, the local women need someone to dominate and sexually colonize them given that their males are too cucked. And we know that beggers ain't choosers so I suppose they take in anything that is foreign.

Apart from maybe integrals, what's the problem with using rationals? Epsilon-delta definition of limits/continuity/differentiation still work for rationals

>>8889714
Intermediate value theorem is false for continuous functions Q -> Q.

But there is a way to work constructively with the real field, and that's how I know Wildburguer is a hack and a fraud.

>>8889598
I can sympathise with wanting to try and build rational mathematics, because it's (in some ways) simpler and neater than the reals and no-one else is really doing it.
I have no idea what the fuck Wildburger's deal with limits is. Yes, historically they were pretty damn fuzzy, but I'm under the impression that the modern construction is watertight.

>>8889744
The modern definition is rigorous but unintuitive, and constructionists like Wildberfer disagree with it on principle

It's funny that there is a totally algebraic treatment of calculus with infinitesimals but you have to fuck around with ultrafilters which would drive Wildberger up the wall.

File: math maymay.jpg (1016KB, 800x2000px) Image search: [Google]

1016KB, 800x2000px

>>8889784
10 buckaroonies says wildberger will invent the hyperreals, but will define [math]\epsilon[/math] as a very specific rational number. Probably [math]\frac{1}{10^{200}}[/math] since that's his favorite.

>>8889811
Kek'd at pic

>>8889811
Does Wildberger really try and argue mathematics from physical analogies like that? Because I'm not even a math student, and that's still obviously pathetic.

the only problem for him is that he bases is new maths on QM which is done by classical math

>>8889874
Bahaha

The solution for differential calculus already exists but is 100x more complicated than typical analysis.

Deformation Theory over finite bases should work mostly within his parameters.

File: LARGENUMBERSBTFO.png (1MB, 1602x900px) Image search: [Google]

1MB, 1602x900px

>>8889848
Yep
https://www.youtube.com/watch?v=z_IAB5T0Qoo&index=1&list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
He talks about it a bit around 37 minutes in

>>8889914
>The natural numbers are finite, because you would run out of space to write big numbers.
This is the most retarded idea I have ever heard in mathematics. I don't even know what to say.

>>8889989
as crazy as he is, he didn't just pull these out of his ass. he actually goes pretty in-depth with his explanations and reasoning.

>>8889874
Don't worry he's going to rederive QM one of these days as a part of his math foundations series

File: 1461830882559.jpg (85KB, 1012x712px) Image search: [Google]

85KB, 1012x712px

>>8889598
It's happening! Rational calculus is almost here! The madman actually did it!

>holds up right triangle with height and length 1

uhm, try again sweetie

>>8889617
He should write a book about "Conceptual Math".

>>8890219
You mean quadrances 1, 1 and 2 right?

File: melNPLi.png (21KB, 783x131px) Image search: [Google]

21KB, 783x131px

uh /sci/ btfo?

>>8890286
Rejecting a question because you don't like the answer isn't terribly impressive.

>>8890286
For someone who champions realist view of mathematics it's especially strange to assert that it's nonsensical to talk about the length of a line.

>>8889663
the best mathematician in the world atm is australia

turns out this dude is actually a talented mathemtician. i dont agree with his reasoning but its pretty creative and maybe something useful will come out of it one day

>>8890362
>the best mathematician in the world atm is australia
He fucked off from Australia though.

What's the quadrature of a circle with a radius of quadrature one?

>>8890360
Even in mainstream mathematics there are one-dimensional sets who can't be assigned a length. For example
https://en.wikipedia.org/wiki/Vitali_set

>>8889598
Like he said, idiots. This isn't just for people who agree with his skepticism regarding infinite processes. For one, I'm very excited to take the course because it should be easily applicable in numerical analysis and the approach seems interesting in of itself.

>>8889598
I just don't fucking get it. He looks reasonable enough, why not divert his abilities into something more useful? Why the fuck would you want to do math without reals? What's the problem with irrational numbers? Next he won't do complex analysis because he doesn't like imaginary numbers.

>>8890367
No worries, Wildburger sidesteps these problems by defining quadrance for line segments only.

>>8890366
yeah well no shit he's not retarded

>>8890379
It's useful because computers can't do math with reals.

>>8890394
Well, good thing math doesn't care about whether computers like it or not and computers can always round up to a good margin of error.

>Captcha: MontREAL 3410

>>8889605

Maths.

Criticized with ad hominem attack.

You are like the ignorant who mocked Charles Darwin. Fool

When I see such comments I become interested in the subject matter, for clearly this Wilderberger guy has rustled your jimmies, and whatever upsets fools like you is frequently worth investigation.

>>8889732

Yeah thats why you are so famous.

>>8889989

Its a little bit over your head isnt it dear? Now why dont you have a nice glass of warm milk and go to bed?

>>8890360

yes, yes, its all just too much isnt it? Now grab your teddy and go to bed son.

>>8890416
>>8890420
>>8890421
>>8890425
Wildberger...

>>8890379

Yes, just ignore it all, really, dont let it bother you. Now, do you need some help or can big boy tuck himself into bed all by himself?

>>8890428

No. Just someone who isnt as thick as (you) these fuckwits.

I hope (you) these fuckwits are just high school dicks, not University level students, becasue then I could just blame it on under development of cognitive reasoning.

>>8890404
t. undergrad in math

>>8889989
>This is the most retarded idea I have ever heard in mathematics.
Why?
It is as reasonable as to assume that they are infinite.

>>8889605
>is he for real?
are you retarded of course he isnt for """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""real""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
possibly he "is for rational".

>>8890486
>It is as reasonable as to assume that they are infinite.
It's not an assumption at all!
The infiniteness of the (set of) natural numbers follows immediately from their definition. Claims about what you could or couldn't fit into the physical universe are completely irrelevant. The universe could be so small that the largest quantum that fits is "eight", and still nothing in mathematics would change - because mathematics isn't a description of the universe.

Suppose someone DID sit down and determine "Wildberger's Number" (W), the largest value that can be represented in any way in this universe. As any child who's played "who can think of the largest number" knows, W+1 is also a perfectly valid number, and it only takes thee characters to write.

>>8890486
Every time our universe grows a tiny bit, a new number come into existance. Isn't that beautiful?

>>8890528
You dont understand mathematics at all.
I really have nothing else to say, you are discrediting a theory based on your personal beliefs and your misunderstandings about the topic.

Of course in the standard definition of the natural number the set is infinite, but that doesnt invalidate any other theory where it is not.

>>8890528
Well, Wildberger says that W exists, but W+1 doesn't exist. Ultrafinitists don't just reject actual infinities, they reject potential infinities and give a hard limit to how big a number can be. Of course, they never manage to give a satisfactory answer to what that hard limit should be.

>>8890649
>Define addition to be adding n amount of extra lines for addition of n. BTFO

>>8890637
>You dont understand mathematics at all.
Thanks

>Of course in the standard definition of the natural number the set is infinite, but that doesnt invalidate any other theory where it is not.
Right, but were not talking about those other theories. Wildberrger is using (AFAIK) traditional natural numbers, and their "existence" isn't tied to what can be written somewhere in the universe.

>>8890649
>Wildberger says that W exists, but W+1 doesn't exist.
Sure, but I don't see how that's a supportable view. The expression W+1 obviously exists, and so long as W is a natural number then W+1 is necessarily both larger and also a natural number. The question of "would it fit, if you wrote it out some other way" seems irrelevant.

>>8890670
Wildberger doesn't believe in the existence of infinite sets.
For him there are only finite many numbers and thus there's a largest number W such that W+1 isn't defined anymore.

>>8890637
>that doesnt invalidate any other theory where it is not.
But no one is able to establish an acceptable alternative, they never went beyond "real big numbers can't fit inside my computer".
On the other hand, constructive mathematics provides you with tons of different alternatives, so you can't blame mathematicians for not wanting to study your theory, it's just that you never had any to begin with.

Literally in denial of something solved 3000 years ago

>>8890679
>Wildberger doesn't believe in the existence of infinite sets.
Okay, then that's just silly. I'm not even sure it's WRONG in any formal sense, it just seems needless and contrarian.

>>8890697
What? Just because something has not found any practical uses doesnt mean that it is useless, mathematicians can study whatever they want, but not considering alternatives creates an inferior mathematics.

I am not even an (ultra-) finitsits, but still such Ideas are completly valid within mathematics and it is quite possible that they will find their uses.

>>8890679
>For him there are only finite many numbers and thus there's a largest number W such that W+1 isn't defined anymore.
As soon as I see a formal axiomatization of such a system, I will consider taking it seriously.

>>8889625
He understands them perfectly, but you wouldn't know, as you're not a mathematician.

Wouldn't Wildberger's point of view screw up algebra? For example, + would no longer be an operation on Z, so Z loses it's ring structure.

>>8890649
The hard limit in my view should be any number with a finite number of digits. The set of real numbers obviously includes numbers with infinite digits, and in those numbers it is impossible to do many algebraic operations on them computationally. All math should be algorithmically possible in finite time.

>>8891052
You realize there is no limit to the integers and all integers have finite digits right? I'm not sure you understand what is meant by the limit in this case. Also, if you ignore numbers with infinite digits then you ignore all infinitely repeating rationals. But this is competent arbitrarily as it depends on what bare you're in.

>>8891105
*But this is completely arbitrary as it depends on what base you're in.

>>8890721
>>8891045
>I don't know what a semiring is.

Seriously though, Wildberger's insanity goes beyond just identifying all numbers bigger than W.

>>8891120
A semiring is a ring without an additive inverse, but that's not the problem in Wildberger's theory. The problem is that a+b is not always defined in Z.

How does Wildberger define the concept of cardinality?

>>8889605
FFpFpbFpbp

It would be interesting to see the differential equations in QM to be done without the use of infinities. I wonder how this would affect many of the inconsistencies and infinities arising in QM's interactions with relativity and the theories of quantum gravity in general.

>>8891132
It's one of the problems. Wildberger says to say all numbers bigger than W are "too big". So just make a new number (equivalence class) for those and do arithmetic like you do with infinity in elementary calculus. I know it's annoying, but sometimes reading the intro to a Wikipedia page when someone mentions something is not enough to contribute productively to the conversation.

>>8890721
Wildberger doesn't believe in axioms either

>>8889625
>>is he for real?
>yes

wait hes AGAINST reals

File: opengl_demo.png (29KB, 705x533px) Image search: [Google]

29KB, 705x533px

I want to code my own raster painter application that paints in a 3D space.
how hard would be to code a basic paint application like mypaint or paint but that paint 3D pixels rather than 2D pixels?
Also how hard would be to also implement in said application basic vertex modeling, like a basic blender?
Also, in the same application being able to draw vector lines, like SAI?
And have basic 3D toon rendering capabilities of the previous shit.

I would appreciate a list of what topics, both math and CS do I need to learn before trying to make this.

Many thanks.

Since there's no good solution to make good 2D using 3D software and I need a solution for my own games, and since I'm starting to learn opengl and 3D computer graphics, I've made a document where I explain all the requeriments I need as a 3D artists and 2D artist to mix both worlds in a 3D solution.
I suppose people here would be interested into my ideas.
I think many of them could be possible to implement in blender, but I don't see them in any 3D software, since they came from my 2D experience with diferent 2D software.
Pls rate.
https://docs.google.com/document/d/1t2J63EI_WfcPbff3X3hEi--7GB1WN9W6pTOVthX-OH4/edit?usp=sharing

Many of the end ideas for NPR shit are there, like having more than one specular you can edit (basically projecting a circle shape that indicates the light), having a texture for shadows and lights you can paint (like normal modifiers), having diferent render passes for every specular and shadow layer, and treating the shadow as if it were a projected polygon skin onto the mesh you can paint over.

I have so many ideas for NPR rendering, that I feel there's not curent software that make them possible, so that's why I want to make my own software.

>>8890379
>>8889744
>>8889605

Because it's an ambiguitiy

when you talk about doing math with reals you talk about math that can't even exist. Math that you can't even compute.

That leads us to stupid results like banach-tarski.

As for infinite sets: that's just a dumb way of thinking about things. Why not say "n is of the type integer" instead of "n is contained in a set that can't exist"?

i'm unironically watching his lectures and they're pretty clear

>>8891346
I don't think anyone is arguing that he's a bad professor. Just that some of his ideas are very out there.
He does a good job in distinguishing when he's gonna shill his ideas in lectures, so he's not bad. He's just a bit delusional
"Ok so for this next section, we're gonna use the hip and trendy new idea that's taking over the internet 'Rational Trigonometry', it's alot better than what they taught you in school and I predict it'll take over the world soon"

>>8891169
That's just his retarded political rhetoric.

>>8891247

Not easy

>>8891263
>mathematical existence is about computability
hurrrrrrrrrrrrrrrrr

>the result is unintuive therefore the method is wrong
durrrrrrrrrrrrrrrr

>>8891393
At the vert least math as applied to the real world should be computable, let the pure mathematicians live in their made up fantasy lands.

>>8891405
Irrationals are applied all over. Infinities are applied all over. Computability has nothing to do with general application, it has to do with application by computers. Why should computers be the arbitrator of math?

>>8891417
Show me physical proof of an irrational number that is countable in finite time.

How can he be a professor if he don't understand high school maths?
Why the uni didn't fire him for making these dumb videos?

>>8890371
Yes, and there are functions discontinuous at infinitely many points and yet it doesn't mean there are no continuous functions

>>8890679
But W+1 is a valid definition of a number

>>8891425
Proof of a number? That makes no sense. A number is not a theorem. Try again.

>>8891455
I'm talking about physical proof of these numbers being present in reality. We can clearly see natural numbers everywhere. No measurement is infinitely accurate so numbers which require infinite accuracy are unscientific to apply to reality.

>>8891458
>I'm talking about physical proof of these numbers being present in reality.
Numbers are not present in reality, they are used to represent things present in reality.

>We can clearly see natural numbers everywhere.
No, you can clearly see how natural numbers can be applied to reality. You can also clearly see how irrational numbers can be applied to reality.

>No measurement is infinitely accurate so numbers which require infinite accuracy are unscientific to apply to reality.
All numbers require infinite accuracy. You are so confused. 2±0.1 is not a number.

>>8891467
>Numbers are not present in reality, they are used to represent things present in reality.
That's overly pedantic, but to clarify I mean countable representations of human defined grouped objects with their boundaries defined in time and/or space.
>You can also clearly see how irrational numbers can be applied to reality.
They cannot be applied without resorting to techniques of approximation, there is no physical boundary which can exist that fully represents them. This is because as far as we know everything measurable is quantized.
>All numbers require infinite accuracy
For use in physical measurement they just need to be believably accurate. So the fundamental units should be defined at whatever scale of measurement we can be confident will never change no matter how many times the same measurement is done.
>2±0.1 is not a number.
It can be used as one.

>>8891393

The method was correct given the flawed definition of the reals

Also math by definition cannot deal with things outside of being computable.

>>8891487
>I mean countable representations
What does it mean for a number to be countable? Only sets are countable.

>human defined grouped objects with their boundaries defined in time and/or space.
No numbers are defined in time and/or space, so I still don't see what you're talking about.

>They cannot be applied without resorting to techniques of approximation, there is no physical boundary which can exist that fully represents them. This is because as far as we know everything measurable is quantized.
There are several theorems in physics and chemistry that use exact irrational numbers. For example certain exponential relationships can best be described using e.

>For use in physical measurement they just need to be believably accurate. So the fundamental units should be defined at whatever scale of measurement we can be confident will never change no matter how many times the same measurement is done.
And what does this have to do with irrational vs. rational numbers? If my equation using e is accurate no matter how many times we measure, this confirms that our exponential model is correct.

>It can be used as one.
That doesn't respond to the point. The number two is just as exact as the number pi.

>>8891521
>The method was correct given the flawed definition of the reals
I look forward to you publishing this flaw and disproving the reals.

>Also math by definition cannot deal with things outside of being computable.
Of course it can. We can "deal" with pi even though computers cannot. We do it everyday.

>>8891487
The stance that at one hand math should be subordinate to reality, but then physics should throw out useful math because it does not conform with your axioms is incredibly hypocritical and stupid.

>>8891524
What does it mean for a number to be countable? Only sets are countable.
The numbers are the accumulated results of a counted set where that set is defined by something(s) that can be observed and measured in reality.
>No numbers are defined in time and/or space, so I still don't see what you're talking about.
The units the numbers apply to are.
>There are several theorems in physics and chemistry that use exact irrational numbers. For example certain exponential relationships can best be described using e.
Yet when those results are checked by measurement we don't get an infinitely precise result. That means these relationships are truly only using a finite approximate of e.
>And what does this have to do with irrational vs. rational numbers? If my equation using e is accurate no matter how many times we measure, this confirms that our exponential model is correct.
It confirms the exponential model is correct up to a certain approximation of e, but it can never truly confirm whether the exact number e is what is really underlying reality. Assuming that is purely hypothetical speculation.
>The number two is just as exact as the number pi.
Except predictions which match observations using the exact number 2 can be made, whereas predictions using the exact number pi can not be made unless you approximate pi.

>>8891549
>The stance that at one hand math should be subordinate to reality, but then physics should throw out useful math because it does not conform with your axioms is incredibly hypocritical and stupid.
I'm not against any math that is useful for solving problems in physics, but when usefulness overtakes accuracy there are going to be disastrous consequences.

>>8891532

you couldn't disprove the reals because they are basically an axiom

>>8891576
>The numbers are the accumulated results of a counted set where that set is defined by something(s) that can be observed and measured in reality.
Again, no numbers are defined with respect to physical reality. This is an arbitrary and vague demand.

>The units the numbers apply to are.
We're talking about numbers are we not?

>Yet when those results are checked by measurement we don't get an infinitely precise result. That means these relationships are truly only using a finite approximate of e.
No it doesn't. The precision of the measurement has no effect on the relationship itself.

>It confirms the exponential model is correct up to a certain approximation of e, but it can never truly confirm whether the exact number e is what is really underlying reality. Assuming that is purely hypothetical speculation.
As I already pointed out, the same could be said about any constant, rational or irrational. So your argument fails.

>Except predictions which match observations using the exact number 2 can be made, whereas predictions using the exact number pi can not be made unless you approximate pi.
Nope, you already admitted measurements don't have exact precision, so you can't match any prediction exactly.

>I'm not against any math that is useful for solving problems in physics, but when usefulness overtakes accuracy there are going to be disastrous consequences.
How can usefulness overtake accuracy?

>>8891595
Then why call their definition flawed? It's immature political rhetoric, which is the only thing that makes Wildberger standout. This is very useful for attracting the attention of naive undergrads and contrarian laymen, but not so much for actually doing math.

what is the equivalent of the Fourier transform in Wildbergerland

>>8891641

He worked on fourier analysis for years

>>8891641
fourier transform is computable

>>8889605
>it's a piggot oinkery
what did anon mean by this?

it's just amazing how butthurt people get about finitism

>>8892433
Pleast stop, I'm literally dying over here.

>>8890360
Underrated post. Fully agreed.

>>8890721
IIRC, Wildberger also objects to formalizing systems in that way, preferring intuition. Yea, he's weird.

>>8890286
this seems especially easy to refute? He has no problems with line segments and rotations of the plane right? So why shouldn't I be able to assign a length to that which is a straight vertical line segment?

File: cubictangentparabolasnevercross.gif (935KB, 995x530px) Image search: [Google]

935KB, 995x530px

>>8889608

https://youtu.be/Js2mwsHc4p4?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf

Heres a proof of calvieris quadrature formula by him that uses no analysis.

He also has videos on the algebraic derivative around math foundations 70

Pic is something I did with the methods he lays out

>>8889714

Heres a video of wildberger proving Calvieri's Quadrature formula for a general field, no analysis or reals required.

https://youtu.be/Js2mwsHc4p4?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf

File: images.jpg (10KB, 268x188px) Image search: [Google]

10KB, 268x188px

>>8889732

You sound like you dont actually understand his arguments. A proof of his about Calveiri's quadrature formula is posted twice in the thread, its valid over I general field, I suggest you watch it.

The thing about rational triganometry and algebriac calculus is that you dont have to reject infinity or reals if you dont want to, they are still superior theories of their respective disciplines and will enrich your knowledge>

>>8890379
Here is a 4 part series on Quaternions viewed rationally.

https://youtu.be/uRKZnFAR7yw?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf

You should consider evaluating some of his arguments and methods before you continue to make yourself look stupid.

>>8892940

Consider that for every line segment, there is a unique qudrance. for every quadrance, there is two possible line segments, which allows for orientation of segments, and allows one to more effectively capture geometry algebraically.

This should really be the most convincing argument though, the truth is you really should just watch some of his rational trig playlist and evaluate it for yourself. https://www.youtube.com/playlist?list=PL3C58498718451C47

I prefer qudrance over sqrts

>>8891425
irrational numbers are practical, that's why they exist. they don't need to be computable.

>>8893098

Quadrance contains all the same information, yet it is also represent able completely, and is the primary object of rational trigonometry, which is the natural and correct conception of the subject.

>>8893121
maybe so, but you still need irrational numbers for other things. show me how to find the area and circumference of a circle, knowing just the diameter without irrationals, and i will be convinced

a piggot oinkery

can't stop thinking about the piggot oinkery

>>8891595
The reals are not an axiom though, you can construct them just fine using the integers and standard ZFC theory. (You create the rationals as Z's fractions field, and then the reals with Cauchy's construction...)

>>8893273
https://www.youtube.com/watch?v=3cI7sFr707s

piggot. freakin'. oinkery.

>>8893308
Most MathFoundations videos attack things he doesn't like based on his strawman definitions for those things.

>>8893681
That's total bullshit. He picks apart actual definitions very carefully. Show me one example of a strawman he's made.

>>8893692
https://www.youtube.com/watch?v=_6B2PUn99Bc

>>8893697
so what is your problem with his exposition?

>>8893701
He keeps talking of function as a rule/procedure and claims functions are broken because there is no clear definition for what a rule/procedure is. Fair enough, but functions are not defined like that.

>>8893706
>Fair enough, but functions are not defined like that.
how do you define them then? please do not say it is some relation with an extra requirement

>>8893697
>>8893706
That's extremely pedantic and missing his point.

>>8893711
A function is some subset of the cartesian product of its domain X and its codomain Y such that for all x in X there is exactly one y in Y.

>>8893712
He has no point. His examples of "weird" functions are avoided if not using his strawman definition. The formal definition of a function was developed to get away from the informal notion of the function as a rule/procedure.

>>8893721
yeah that works in set theory, which is precisely the result of the people who want to formalize what a procedure is, within classical/naive set theory.

a function is really another name for a procedure which finishes in constructive math and which may not halt in classical math, then a few people choose to formalize it with sets

>>8893721
>A function is some subset of the cartesian product of its domain X and its codomain Y
In other words, a relation
> such that for all x in X there is exactly one y in Y.
with an extra requirement.

>>8893735
That's the definition.

Another one of his strawmen is with real numbers. He talks of them as being defined as infinite decimals at first, justifying this with "well students are first introduced to them like this." So, all of his criticism on reals based on this strawman definition is worthless. Way later he actually takes a look at actual definitions (Cauchy & Dedekind) where his criticisms boil down to "I don't like infinite things."

>>8892924
The reason we use axiomatizations is that history teaches that when you do math without a formal specification, you'll end up with all sorts of amusing contradictions and paradoxes you didn't see coming. And of course there is no point in writing formal proofs without a formal baseline.

Does he have an alternative solution in mind to avoid these problems? Or are we to take all his work as contradictory until further notice?

(I know you're just the messenger. My snark is not aimed at you, but I find it hard to suppress it entirely.)

>>8893744
Did you even watch the video on Cauchy sequences? The most damning observation he makes IMO is the fact that by the equivalence classes of Cauchy sequences definition, all real numbers are exactly identical.

File: Hott_book_cover.png (97KB, 220x317px) Image search: [Google]

97KB, 220x317px

>>8893749
Not the guy you're responding to, but there is the option of developing axiomatizations that respect intuition.
One option (not perfect, but a step up over what we have now) is to base your axioms on the "semantic" properties of what we want our mathematical structures to DO, rather than a "syntactic" bottom-up approach of what they should BE. For example, this would entail axiomatizing the reals as a complete Archimedean ordered field, instead of an equivalence class of infinite decimal sequences. The former has the advantage of giving you precisely the properties and operations of R that you want.

An even better option is to invoke the Curry-Howard correspondence: formalize proofs (and functions) as first-class, syntactic objects which leads to a model that can be interpreted semantically as characterizing R (up to equivalence). Pic related is probably the biggest /sci/ meme that does this.

>>8893749
What are some examples of contradictions and paradoxes that axiomatization ameliorates? Specifically ones that don't involve infinite sets or infinite processes.

>>8893788
>Not the guy you're responding to, but there is the option of developing axiomatizations that respect intuition.
Yes. But you still need to write them down somewhere, or you'll find that your intuitions differ from mine; leading to interminable debates at best, and long derivations that use your intuitions at one point and mine at another to conclude contradictory things for no apparent reason at worst. So the philosophy of not axiomatizing things at all seems very silly indeed, even if you have good reasons to dislike a particular axiomatization.

>>8893815
Most of the classic paradoxes from around 1900 apply. The liar paradox, Russell's paradox, Löb's paradox (more recent, but still), etc.

>>8893755
How does he come to that conclusion? Because he doesn't like infinity.

>>8893842
>Yes. But you still need to write them down somewhere, or you'll find that your intuitions differ from mine;
but that is all there is : different intuitions and each intuition is more or less formalized by some guys

>>8889714
You need to re read your real analysis book. Without irrationals, you can't garuantee cluster points exist so you can't say anything about limit definition of continuity. Of course every f is continuous at every isolated point c belonging to its domain but that's not very useful. Additionally, when the irrationals are removed from the reals, the reals are no longer complete and you can't use the archimedean principle which means delta epsilon proofs for limits of sequences no longer hold.

At the end of the day, numbers are not real objects. They can be represented by real objects but to say that every atom represents 1 number but can't represent 2 or more atoms is ridiculous.

>>8890360
>>8892940

I think I saw this video.

When he says "length of a line" he is referring to some ancient text by Euclid IIRC. Euclid thought of numbers as representing lengths of lines.

All he is saying here is that he doesn't believe in reals.

File: 2017-05-09-002739_837x378_scrot.png (57KB, 837x378px) Image search: [Google]

57KB, 837x378px

>>8894460
No, he's responding to a comment in the algebraic calculus video.

Guys please teach me how to compute tax brackets

>>8894491
watch wildburgers MathFoundations
https://www.youtube.com/watch?v=91c5Ti6Ddio
you'll learn everything

>>8894475

Well it's still just him saying he doesn't believe in reals

>>8894475
He's wrong about this. It's pretty trivial to prove that any line in a plane is lebesgue measurable and thus has a well-defined length.

All this shit is disproved by an easy topological theorem..that cardinality of reals is greater than cardinality of Naturals. For each real interval i can find more and more numbers in it.

>>8894656
+

>>8894679
What the fuck was the point of this post? I guess you're trying to say you agree with me, but why bother posting that in the first place? You could at least have used a real sentence.

Can someone give me a quick rundown of why Wildberger is so autistic about the reals?

Like is there a specific part of a specific video you can link me to where he goes into it?

>>8894686
Dude just chill. Im doing Calculus on Manifolds and I upvoted you because i study this right now.

>>8894686
I went for a natural sentence bro

>>8894686
+

everything is actual one, arithmetic and every other number isn't even real

>>8894686
unsubscribed until you clam the fug down

>>8894696
>>8894698
>>8894700
>>8894706
This is my first time on /sci/, obviously coming here was a mistake. Seems like most of the people on here are still in school.

By the way, I have a Ph.D in Music from the University of Southern California. Do you have a Ph.D? No? Then shut the hell up.

>>8889754
What's unintuitive about convergent sequences and functions on them?

>>8894771
The delta-epsilon definition of a limit takes years to understand. It's anything but intuitive.

t. comp sci major

>>8889914
The issue I get with ultrafinitists and the concept of not being able to write a number because of the size of our universe, is that it's so easily counteracted. Our base-10 system is merely one construction of a number, defined by specific processes, and we can express numbers in all sorts of different, well constructed, well defined ways, that no matter what number you propose is the "largest" number, we can find a number bigger than it and work with it easily.

That being said, I think there's merit in trying to build constructive systems for certain types of mathematics. Even if they're redundant, it can give us more understanding of those systems, and often times constructive approaches are more immediately applicable to things like computational calculation.

>>8894781
I mean, only if your teacher doesn't give a shit and you don't spend time looking things up yourself.

>>8894693
I haven't looked into it much, but I think he's probably an intuitionist, and specifically an ultra-finitist. He doesn't think the Reals as we define them is actually well-defined

anyone else glad that we use notation like irrational and imaginary to weed out the brainlets?

>>8894782
There's a thing called proof mining which basically turns proofs, especially in analysis, into upper/lower bounds, e.g. Euclid's proof of the existence of infinite primes gives you a lower bound for the nth prime number.

But Wildburguer is too much of a beta brainlet to be interested in real foundational research and wastes his time attacking superior mathematicians instead.

File: haha.jpg (41KB, 562x437px) Image search: [Google]

41KB, 562x437px

>>8894720
>Ph.D in Music from the University of Southern California

>>8894806
It's nomenclature not notation you illiterate.

>>8893842
>The liar paradox, Russell's paradox, Löb's paradox (more recent, but still), etc.
Except those paradoxes come out of axiomatics, which is the point.

>>8893878
No, that's not how he comes to that conclusion.

>>8893945
https://www.youtube.com/watch?v=K4eAyn-oK4M

>>8894656
IDK if he's specifically gone into the problems with measure theory yet, but I'm sure it comes down to his problems with analysis in general

>>8894782
https://www.youtube.com/watch?v=p9xX-Jpsr_E
https://www.youtube.com/watch?v=I0JozyxM1M0

Also for fun:

https://www.youtube.com/watch?v=LJR24_Povzw
https://www.youtube.com/watch?v=DhJ_sp3Kx_E
https://www.youtube.com/watch?v=2ypz1fydnT4
https://www.youtube.com/watch?v=S1CB3_1KQGI

>>8894887
He recognizes great mathematicians, he just points out where they're mistaken

>>8896026
At his first slide he's written:
>We'll also have to venture into the never-ever land of `infinite sets' to critique `equivalence classes.'
His argument is that all real numbers are the same because it would take an infinite amount of work to inspect they're different.

Basically stop pretending you know more about mathematics than this guy you fucking idiots

>>8896053
How would they look different even if you could hypothetically do that infinite amount of work?

>>8889914
If what he's saying is true then would he seriously claim that, for instance, the number of permutations of all atoms in the universe doesn't exist?

>>8894686
+

>>8894946
That is one vintage meme.

>>8894720
They are underage since my brother is and uses + as way for chatting.
But hear me out:
>Ph.D in Music
If you can hear how ridiculous it sounds.

File: The Topos of Music - Mazzola, Guerino.png (107KB, 645x829px) Image search: [Google]

107KB, 645x829px

>>8896113
>he hasn't even begun to comprehend the principles of topological music theory

bumpin for the piggot oinkery

>>8894781
Just goes to show you that CS is populated by low IQ pajeets

>>8896206
Yeah so hard my pepe goes wee wee.

File: real math.png (17KB, 702x387px) Image search: [Google]

17KB, 702x387px

>>8890394
They can though.

>>8896974

They still can't

e is not a letter it is a number. One that happens to be infinitely long and physically cannot exist

>>8894475
I love how as soon as someone brings up something simple and intuitive that his system can't handle he just goes "W-well who even says its a thing in the first place??" As though sticking his head in the sand when a problem comes up "proves" his shit is water-tight.

>>8897386
Except it can handle it, and you would know that if you actually watched his videos.

>>8897089
express it as a fraction then brainlet

>>8896974
How do they deal with noncomputable reals?

Also there are serious problems with algorithmic definitions of numbers, one of the biggest being that equality can't be established in general.

Wilberger is why I come here

INFINISTS BOYS GETTING KEKED AGAIN

GOD BLESS WILDBERGER

>>8898298
initially read "KEKED" as "NAKED". it's also weird how cuck is only filtered when it's all caps KEK

>>8898167
He literally says right there in that image that the question doesn't make sense. If he did have an answer why didn't he give it?

>>8897089
>Can not be accurately expressed as a decimal number
>Therefore can not be used by a computer
Found the brainlet, you probably think computers can not work with numbers like 1/7 either because there's no finite decimal representation

Ever heard of ways to describe numbers apart from the decimal number system? Probably not since you're still in high school

I remain puzzled over the circle of diameter 1.
-people claim that numbers exists because ''I see two trees before me so the number 2 exists same thing for the next naturals''
-people who want to ascribe a perimeter to the circle of diameter 1 claim that it is \pi
-people claim that \pi has infinitely many digits
-so clearly creating circle of diameter 1 is a way to represent in a finite way the number \pi which has infinitely many digits

so what is the problem of the people who do not believe in the reals?

>>8898193
>How do they deal with noncomputable reals?
The same way humans do: They don't try to compute them.

If you have a description of a number, computers can work with the same description of a number - for example, computers can calculate with infinite sums just fine.

>>8898419
He has an entire series of videos devoted to doing trigonometry with only rational numbers

>>8898428
where did that person mention decimals?

>>8898436
>They don't try to compute them.
Meaning they can't deal with them.

>computers can calculate with infinite sums just fine.
A computer can never calculate an infinite sum.

>>8898450
>>They don't try to compute them.
>Meaning they can't deal with them.
By the same logic, mathematicians can not deal with irrational numbers either.

>>computers can calculate with infinite sums just fine.
>A computer can never calculate an infinite sum.
I said they can calculate WITH infinite sums.
And your post is just wrong, see
>>8896974
Infinite sum, and the computer gives back the correct result

Though there may be some infinite sums computers can not calculate (i.e. infinite sums humans can not calculate either)

>>8898449
He obviously thought decimals are the only way to describe numbers, otherwise he wouldn't have said that "e happens to be infinitely long and physically cannot exist" (which is by the way a really stupid statement, since numbers don't physically exist in the first place)

>>8898461
>By the same logic, mathematicians can not deal with irrational numbers either.
That's the point, though...

>Infinite sum, and the computer gives back the correct result
All it gives is five times a letter. Doesn't say much about the number itself.

>since numbers don't physically exist in the first place
They physically exist as much as words do: as ideas in your head and writing on a page.

>>8898465
>That's the point, though...
Then your point is wrong.

Ever heard of a mathematician saying "I can not compute this, I would have to calculate with irrational numbers"? Me neither.

>>Infinite sum, and the computer gives back the correct result
>All it gives is five times a letter. Doesn't say much about the number itself.
So you can not calculate what that x + x + x = 3x unless you know what x is?

>>since numbers don't physically exist in the first place
>They physically exist as much as words do: as ideas in your head and writing on a page.
5 is a an idea in your head and can be written on a page and you can do calculations with it and it is a number
[eqn]\sum_{n \rightarrow \infty} 1/n![/eqn] is an idea in your head and can be written on a page and you can do calculations with it and it is a well-defined number by mathematicians point of view, but you say it is not a number

Why?

>>8898486
>but you say it is not a number
>Why?
Wildberger prefers a definition of number that allows proof of equality in general. An algorithmic definition of number does not allow this.

>Shitting on Wildberger
I am discussed by all of you.
Pathetic bunch of bootlickers.

>>8898600
I ain't arguing with wildberger, I'm arguing with some anon who says computers can not calculate with irrational numbers