"perfect arguments don't exi-"

yes

He's so retarded. He should be clear that he is proposing an alternative to standard mathematics. Not a superior alternative, not a correction in some erroneous reasoning or proof. Mathematicians accept the concept of infinite sets, he doesn''t. This says nothing about logical consistency and it's pathetic that he thinks so. Does he not understand axioms? Oh yes I forgot he doesn't like axiomatics either. The guy's a complete retard

Just simply define forward as being the direction you are travelling instead of a cardinal direction based upon your orientation, and you can move in any direction :)

*zeno's "forward" but actually laterally away* >:^)

>I was wondering just the other day what Veeky Forums thought of Wildberger.
i think it's really fucking cool what he's doing, i just think he'd get more traction if he was a little less confrontational about it.

>He should be clear that he is proposing an alternative to standard mathematics
that IS clear to anyone who spends more than five minutes paying attention to him. go back to your videogames

Can you show me anywhere in the universe or any portion of reality a place where anything infinite exists?

Can you show me the cosmic number line where 1 and 2 are defined and the infinite numbers between them as well?

Can you show me a set of things that is actually meaningfully a set and that proves anything other than that set contains its own contents, without using an abstract example?

Just because you can think of an axiom or because many have thought of axioms, doesn't mean they are right or they must necessarily be true. We have to start somewhere but I respect wildberger for not assuming things that aren't naturally observed.

Uh, no. Don't be willfully obtuse. It's completely clear from his strident tone that he thinks standard mathematics is essentially worthless, or at best accidentally useful but built on a worthless foundation. He's not saying "hey here's an interesting avenue of research to explore just for the heck of it", he's saying that mathematics essentially went off the rails at the end of the nineteenth century and needs to be dragged back on track.

If you spend 5 minutes watching any of his videos you will notice he expresses himself as though he had the moral and intellectual high-ground.
He plainly wants to push the idea that he is right and more importantly standard mathematics is wrong.

I've never seen an abstract number five either, and I'm not sure it's possible to chop things into arbitrarily small pieces, or even chop them into perfectly "equal" sized pieces at all. I can certainly conceive of all of those things as idealizations, but then I can do that for the infinity of natural numbers as well.

If the idea is so outrageously stupid, it should be trivial to prove wrong on the terms of the argument, NOT based on making light of the argument, its propounder, or a related history.

Can you show me on the doll where infinity touched you?
Seriously though, who ever said mathematics has to strictly adhere to some notion of observability?

The same goes for your argument.

Sure, and ideals in science are great for physics or chem 101. But conceiving of things doesn't really mean anything. I can conceive 5 because I have seen 5 things before, and sure I can imagine just the number 5 on its own. But that doesn't mean 5 exists innately nor does it mean that I can truly understand an unrelated concept, like infinity (btw I am skeptical that you can understand that as a concept as well - sure we both know what the word means but knowing a meaning and Understanding aren't the same).

It is. That proof is called "standard mathematics".

Of course, to make it clear exactly where confused thinking goes wrong, you need to tease apart the details of the confusions -- which is not so easy with Wildberger's writing.

>Can you show me anywhere in the universe or any portion of reality a place where anything infinite exists?

Actually yes, when switching on any circuit the current goes from 0 to what ever the current is, and as soon as switch is flipped the current increases by an infinite amount theoretically, and if given perfect conditions, i.e. complete lack of restivity, it would be.

Increasing by an "infinite" proportion is quite obviously not the same thing, unless you think walking from your chair to the cookie jar is also an infinite change

This. If Wildberger wanted to make a real argument, he would say things like "This is how traditional mathematics does it, which is consistent and meaningful under these assumptions. If we want to reject those assumptions, we can build this alternative". Instead, he says things like "I don't understand this part of traditional mathematics, there are no definitions of $THING" "but the definition is right here" "yeah I reject that one, wat do". That just indicates that he doesn't understand what he's talking about, rather than critically considering an invisible assumption.

Correct me if I'm wrong, because I'm more a scifag than a mathfag, but...
Real number : A number which when squared produces a positive result.
Isn't this the commonly agreed upon definition? I didn't think there was any mystery to what a real number was.

> it should be trivial
No, not really, because this is basically epistemology, not math, which is a very fuzzy subject. We're pretty much at philosophical bedrock here, well beyond the scope of easily checkable proofs or arguments.

But that's the point. He acts like he's doing math, and the rest of us are doing nonsense. But he's doing philosophy. When you get this deep down into the foundations, rigor isn't a binary concept anymore, it's a very messy spectrum.

>increasing by infinity, to infinity, until it cant is not infinity

Also its telling that you say ideal and perfect conditions, etc. In reality, in real conditions, it will never happen. If your scenario can literally never happen in reality, why isn't it just a fantasy?

This presupposes the complex numbers. How are you going to define those?

what's wrong with a fantasy?

>back to your fantasy land, physicists.
Never, you're made of strings. Everything shares one electron.

Except if that happened we wouldn't have an electric grid. Your computer is still working, right user?

>why isn't it just a fantasy?
You do realize that self-consistent fantasies are LITERALLY what math is all about, right?

>plagiarises story of Hippasus getting drowned after proving irrationals exist
>perfect argument

Perfect strawman maybe

Nothing is wrong with it, but let's agree that it isn't the same as reality.

I don't really see how it does, but I'll give it a go.
>complex numbers
A real number plus an imaginary number.
>imaginary number
A number that isn't real, so that when squared, produces a negative result.

>In reality, in real conditions, it will never happen.

No, it's rather telling that it behaves in such a fashion, indicating that the axiom of infinity does indeed manifest itself in nature, yet there are also other conditions which guide physical interactions. Being so asinine to dismiss something purely on it needing ideal, yet not impossible, conditions to perfectly observed is even more telling.

Mathematics is a tool used to describe the world. If I have a chicken and I get another one I have two chickens every time. No fantasy there.

It presupposes it because when you talk about "a number that when squared, etc", you need to tell me what a number is.

He pretends there's some logical ambiguity in standard mathematics, which there isn't. He is simply proposing an alternative, he has never pointing out what the "logical inconsistency" he found out about it. His arguments are strictly philosophical ones, such as "mathematics has to be grounded in physics, if there's nothing infinite in the physical world there can't be anything infinite in the mathematical world" this is simply one view and no "problematic logic" or "cloudy thinking" has been rebutted. He insists on using these adjectives though which imply some problem with the current mathematics, it implies his mathematics is more rigorous and a "fix" to the standard mathematics, a stupid implication to make.

Classical geometry is literally wrong in a world governed by relativistic motion (it only works perfectly in a literally empty flat universe) with a causal speed limit, yet we still fucking use it

>what a number is.
This is the point at which you need to start reading dictionaries and stop asking me to tell you.
Number : A value which can be manipulated with other values and specified manipulations.

Fine, that doesn't mean I can't work with reals in mathematics.

This isn't me being stupid, this is just you being a physicsfag and me being a mathfag. Defining what a number is is the kind of shit we do in math majors.

It's not just for the sake of it, though. Actually real numbers (specifically irrational numbers) are a deceptively deep and complicated concept. The only reason you and most people feel they don't need to be defined properly is because, well, we get so drilled with them in school that we're brainwashed into accepting them before we're old enough to realize how fucking weird they are. Look up Dedekind cuts, for instance.

>Defining what a number is is the kind of shit we do in math majors.
That's ridiculous, and I'm really going to need examples of people who aren't making encyclopedias defining what "number" means in the field of mathematics. Not because I don't believe you, but because I don't want to repeat it if it turns out to be nonsense.

>we get so drilled with them in school that we're brainwashed into accepting them
Oh, don't worry, I don't accept them. I think irrational numbers are something so bullshitty that they could only flourish in a field without the scientific method which only occurs in people's heads. No offense.

Actually, imaginary number isn't just a silly concept. It's a silly name. All numbers are imaginary.

Do you know what a field is? Or a ring?

So you don't like math and you don't like the methodology of mathematicians. But perhaps stop pretending you found a smoking gun logical fallacy in all of mathematics?

I get what it means but I'm not sure what I'm supposed to do with it. Rings are to operators as fields are to possible operations?
What do you mention them for?

>you don't like math
No, I do like math. I'm okay with the methodology of mathematicians because that's all that would work with math, since it's entirely mental. I just don't like people pretending words don't have definitions so they can play semantics to sound smart on the internet, like the man in OP's screenshot. [spoiler]It's also really funny to watch mathematicians get mad when I tell them their field isn't pure. [/spoiler]

A ring is a set of elements with two operations satisfying certain properties, a field is a ring with an extra property to satisfy.
The numbers we use are inherently taken to be the elements of a field, which is very explicitly defined.

yeah wildberg is a retard and anyone who isn't a freshman knows this

>implying he isn't pretending to be a retard

Axioms are the reason why we know that infinite sets arent possible. If it was possible Godel's proof would of been proven wrong

I am not involved with "mathematics" in any way really, but, since math shows practical real world application, isn't his "concern with the definition of what a real number is" evidently working backwards?

Doesnt the repeated successful application of these equations based on axioms we "cant" prove, provide foundation for those axioms in a tangible way?

I get what he is saying, that math is based on "belief", but hasn't that belief been tested for centuries? If our definition was wrong, wouldn't we eventually find some sort of logical error preventing us from applying mathematics in real and meaningful ways?

Also, what practical changes does his model suggest? Why is it required and what does it mean?

kinda sorta, it's just to show how the concept doesn't fit his new model (non infinite sets)

he uses stuff we can observe in the real world as a foundation instead, but it's basically the same

we wouldn't really find a logical error, we would just prove that something is "unintuitive" (riemann series theorem is an example of what I mean here) or be unable to prove some conjectures, but the latter is just based on goedels incompleteness theorem which is often used incorrectly

already answered that. it's not required as the way shit's defined now works perfectly fine

>inb4 shitposting

> examples

> real numbers
My first real analysis course started with a construction of the real numbers via Dedekind cuts:
en.wikipedia.org/wiki/Construction_of_the_real_numbers
I believe Zorich's textbook on real analysis starts with such a definition.

> rational numbers
Some people like to go further and explicitly construct the rational numbers. I think this is a bit pointless, but you can do it.
en.wikipedia.org/wiki/Rational_number#Formal_construction
Again, my real analysis 1 course did this. Don't know any textbooks that do, I'm sure there are some.

> natural numbers
You can axiomatize the natural numbers too, rather than treating them intuitively:
en.wikipedia.org/wiki/Peano_axioms
If you don't count axioms as a definition, some people go nuts and construct them explicitly using set theory:
en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers

>riemann series theorem
that never seemed unintuitive to me 2bh
imo it just demonstrates that we cant treat finite operations and "infinite operations" the same way
and we cant really do infinite operations properly irl [spoiler]yet?[/spoiler] so either extra care is required, or sometimes things are ambiguous

Yeah but it's a bit unintuitive that a series [math]a_n[/math] and [math]b_n[/math] can have all the exact same terms but in different places, but [math]\sum a_n[/math] isn't always equal to [math]\sum b_n[/math]

Don't get me wrong, I'm not saying that it's bullshit or anything like that, I'm just saying that it's not intuitive.

well we dont really see "infinite sums" in the real world (other than representations of the unconditionally convergent ones), so there isnt much 'intuition' I feel we can really apply to it

rearranging terms in any finite sum still gives the same answer, which does match our 'intuition'

wildburger threads are the only place I really come across the word intuition

I think the intuition is the idea that if n objects represent the number n, then n objects can represent n*n objects or n^n objects and so on and so forth. So that infinity can exist in a finite universe.

what does >n objects represent the number n
have to do with infinity?
sorry, I really dont follow what you are trying to say at all in this post

how can you nerds find this shit interesting. im'going back to /pol/

actually why don't you try out this new site called reddit, or perhaps you could go LITERALLY ANYWHERE ELSE