Mathematics absolutely btfo

quality shit right there

I completely understand him.

Infinities are pseudo-mathematical unprovable trash that introduce paradoxes in fundamental areas of mathematics such as set theory. The ""axioms"" that we must assume to work with infinities counter all intuition and primal logic in our brains, and are sometimes introduced under the guise of hypothesis/conjectures to be easier to swallow (see for example the continuum "hypothesis").

Infinity does not exist and cardinalities over aleph-null are self-contradictory.

all of this shit flinging and none of you brainiacs can actually prove him wrong

hmm

umm R is contained in C

If he means the algebraic numbers, he should write Qbar not C.

wolframalpha.com/input/?i=z^5 - 2z + 3 = 0

He's wrong though

How can complex numbers be real if real numbers aren't real?

how can math be real when we aren't real?

>Infinities are pseudo-mathematical unprovable trash that introduce paradoxes in fundamental areas of mathematics such as set theory. The ""axioms"" that we must assume to work with infinities counter all intuition and primal logic in our brains, and are sometimes introduced under the guise of hypothesis/conjectures to be easier to swallow (see for example the continuum "hypothesis").
But literally all of this is why I want to do maths, because it just fucking boggles my mind and I WANT TO UNDERSTAND IT. I don't want to reject it, I want to become one with the madness. Fuck off, Wildeberger.

? But there is a very convenient, simple, and powerful definition of infinity in a set K with an order relation without a superior limit, like R or N.

It's the object defined as being superior (as per the order relation we defined) to any object you take in K.

For example, if K is a race of bacteria that always produce offspring and will never go extinct, if my order relation is "xRy means x is a descendant of y", then for any y, I can find an x that validates xRy.

So there is an infinite in this space I just imagined.

(disclaimer, this is me trying to apply some algebra I read. Did I do good anons ?)

Try doing mathematics without infinity. You wont get far,

You just proved you don't understand any of this shit.

There's no proving him wrong on his beliefs, you could perhaps find errors in his work, but it all starts with a belief you can't prove wrong/false.

That's exactly the same as trying to disprove the existence of souls, you can't. That doesn't make believing in souls any less retarded.

>tfw I'm sharing a board with unenthusiastic faggots who don't want to be mindblown by what infinity does to mathematics
It's a pretty bad feeling, desu.

This, but it's the other way around. You're the ones claiming souls.

my sides

real numbers are real

Infinity makes math difficult
See this book: press.princeton.edu/titles/10697.html
>Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics.

Also this: So we are stuck with infinities

How can real numbers be real if rationals are not real?

Yes, by realising most polynomials of degree 5 and above generally do not have closed form solutions.

BRAVO

???

Give me a number which, when plugged into p(r) yields zero IDENTICALLY, not approximately.

I'll wait.

According to the philosophy of mathematics they are, in a sense.

i.e, '1' is not a real thing, but the concept it refers to (a single closed off thing) is real. Same with all positive integers.

Negative numbers are not real in this sense.

...

Pastebin it.

Lol. Nah. The dude is obsessed with the physical act of mathematics. i.e. mathematics is the physical manipulation of symbols. The symbol doesn't mean anything themselves, its how they are manipulated that matters. Guy is obsessed with physicalism, with good reason. That's why he hate infinity. You can't physically carry out the writing and manipulation of the symbols for eternity.

Just do a two-parter

pastebin.com/kSr51BQ6

hmm really makes you think

That's only approximately zero.

Anyone willing to review what I did here please ?

The function is continuous. We see only value yields 0+, the other yields 0-.

Therefore there exists a z so that f(z) = 0.

I am sorry but are you retarded?

Why do you use fucking continuity to disprove Wildberger? Wildberger DOES NOT have a theory of real numbers. Therefore he does not have a theory of real limits. Therefore he does not have a theory of continuity.

Questioning Wildberger is not about proving him wrong through the use of real numbers, it is arguing wether or not real numbers even have a place in mathematics.

YOU'RE retarded. Wildberger isn't wrong, so you can't disprove him. His theory is consistent. But so are the real numbers. His system is just a subset of math where he opts not to use reals. But using them is also perfectly fine.

who gives a fuck
god damn mathematicians are so autistic

>tfw math undergrads on Veeky Forums get fannyflustered by being unable to discredit you

Wildberger mathematics should replace the curriculum, because he's right. Something as simple as "angles" requires intense calculus to explain thoroughly (especially with a system as arbitrary as 360 degrees). Everything he does is built ground-up from absolute first principles, which people would understand if they watched his Math Foundations playlist from episode 1

It's been said that people learn best what they almost already know. Maths is so "confusing" and "weird" to the masses because we're asking them to "just trust us on this" as we take leaps of logic over discontinuities in the progression of mathematical topics. Norm fixes that so one thing naturally flows onto the next as you delve into deeper and deeper topics.

>But using them is also perfectly fine.

Using them is fine but it is kinda pointless to prove him wrong through the use of real numbers.

He will not accept your argument.

Sure, in a normal analysis class then sure. Go right ahead. Prove the FTA through the usual complex analysis tools. But don't bring that to a Wildberger discussion because it is a moot point.

My point is that I could say: "from now on I will only use integers. Rationals aren't allowed" and I'm not wrong, but that doesn't mean rationals are an invalid concept.

He builds on intuition instead of set theory, making for some superficial rigor. In Wildberger's math there are no equilateral triangles and Euclid's proposition 1 is false which of course makes for an interesting universe.

He's not wrong, just his arguments lack rigor

Are you sure about that? I thought he was all about Euclid.

Rational-coordinate geometry lines don't intersect circles and circles don't always intersect which basically makes that well known proposition false.

Euclid didn't use any formal rigor either so it's not the end of the world to prove some of this stuff false but that proposition has been proved with rigor countless times, I'm sure Wildberger has more info on this somewhere or the other finite mathematicians around (there's a few of them).

youtube.com/watch?v=ukiPO4LJqgg

26:00 he talks about equilateral triangles quite happily.

Oh shit by 28:00 he says there are problems. Never mind.

Rational-coord-geometry shits the bed for a lot of geometry but it does make sense for number theory and solves a ton of problems there.

The problem is it is not rigorous though and we had these arguments like a hundred years ago when everybody was tired of conjecture and propositions and wanted formal methods to guarantee something was T or F

FTA is about complex numbers. This old-fag writes about a number [math]r\in\mathbb{C}[/math]. He says no number satisfies the polynomial. Senile dementia.

Also when you use his intuitive ideas for number theory it freakishly 'just works' but on the other hand it can't work since equilateral triangles can't exist in this world. WTFWTF

How does he do Calculus without the concepts of limits and infinity?

the conclusion then for a finitist is that there does not exist a model that satisfies irreflexivity and transitivity (proof that there is no finite model is a nice exercise)

what you've done when you say "there is a race of bacteria etc." is construct a model that satisfies your relation R, however the finitist will deny such a model exists (precisely because there is no finite one, the reason for their reason is axiomatic and cannot be debated on mathematical grounds, and instead must be on philosophical grounds)

Starts around here:
youtube.com/watch?v=vyRFz8J4Y_M&list=PL5A714C94D40392AB&index=71

But you'd need to go back early in the playlist to get what polynumbers are:
youtube.com/playlist?list=PL5A714C94D40392AB

I suggest started at video 1 tbqh

What's his ethnicity? Depending on the lighting he goes from Indian to Jewish to white.

Why do you shill this guy so much?

>reply to a post
>"why do you shill so much???"

Fuck off dickhead, I answered someone's question.

White
t. know him in real life

Noice (Y)

Gently stroke his behind for me sometime. No homo though.

canadian

Funny, he doesn't look Asian.

>intuition
b8

memes

springer.com/gp/book/9789400713468

Algebraic/Geometric point of view. Basically algebraic methods for obtaining a function's associated tangent line, tangent conic, tangent cubic, etc at a point.

Lots of brutal parametric descriptions and he sneaks in a lot of advanced stuff like the algebra of differential forms and changing domain to higher dimensions where infinities in one variable vanish.

>Give me a number x which, when plugged into f(x)=x^2, yields two IDENTICALLY, not approximately.

>I'll wait.

s/believing in souls/not believing in qualia/

Wildberger's entire point is to reformulate math without using irrationals.

Which is to say that Wildberger intends to disregard natural thought processes that produce axioms that require the existence of irrationals in an effort to reformulate math.

Dude, realize he compensates by introducing hardcore shit way early. He is nuts especially since he actually wants this taught to kids but he basically falls back on tensors (especially bilinear forms and symplectic forms) and a lot of group theory over rings in order to make shit work.

Yet he things sin and cos are too hard for our kids.

>natural thought processes
In what regard they are "natural"?

Oh and knot theory. Lots of knot theory.

>And what about explicit examples? Is this not the way to sort out the wheat from the chaff? Yes it is, and all we need to do is open our eyes clearly and look beyond our wishful dreaming to see things as they really are, not the way we would like them to be in our alternative Polyanna land of modern pure mathematics!

Down with the false prophets of infinitesimals !
I mean, his theory is logically consistent, yes, but what's the point ? Without inifinitesimals, don't you "lose" all previous results in analysis, and since almost everything in math is related, almost everything in Algebra and number theory as well ?

Yeah his life work is to reformulate much of that work. The only part he wants thrown out is the infinite set theory of Cantor, etc. Too bad that's the foundation of... everything.

He has dozens of papers and a few hundred videos building up his new math. He uses tensors and linear algebra as his foundations instead of sets (with funky names of course like maxels and such) and it appears he will soon tackle group theory.

He already has a theory of geometry (this is his research area) he even has the start of a geometric theory of Fourier Analysis.

He admits analysis is his biggest challenge, especially measure theory/probability

How can you even use Newton's definition of calculus with his theory ? What about the physics ?

But math doesn't deal with infinities, it deals with things that can be proven to be true for arbitrarily large quantities.

I'd say set theory is all about dealing with infinities.

How so?

All detailed here scientificamerican.com/article/infinity-logic-law/ (from a Quanta journal article reprinted)

You can also pick any present day math journal you want, search for infinity and read the articles by pasting in their link or DOI# into sci-hub there's always infinity dissenters around

>That's exactly the same as trying to disprove the existence of souls, you can't. That doesn't make believing in souls any less retarded.
PS: You can. It's not that hard. The fundamental physics of everyday life is known. The Standard Model accurately describes every experiment that has ever been done on Earth. If QFT is right, and it almost certainly is concerning what happens in our brains, then we know that there are no more particles or forces that have a measurable effect on the human brain, because QFT says that if there was such a thing, we would have noticed it already in particle accelerators.

If there was a soul that did something, it would have to nudge atoms in the brain from time to time. We know that there is no such force, because we've looked really hard, and it's not there. It's the same kind of reasoning that allows us to positively claim that there are no T Rex's walking the planet.

Any rebuttal misses the point, and it's probably fallacious special pleading.

You got Wildberger very wrong. He objects strongly to the view that math is just symbol manipulation. The view "math is just symbol manipulation" is the opposite position of his particular brand of ultra-finitism and mathematical Platonicism.

I'm pretty sure you can have a theory of limits with just Q. Q is dense. Of course, in this system, a Rational-valued function could converge at a point according to the Cauchy definition, but it would not have a Rational-value limit. Other points, the function could converge, and the limit could be defined, and the limit would be a Rational value.

Physicalism

But again, is it infinities that are studied in set theory, or is it rather that "infinity" is just a short-hand way to talk about stuff that can be proven to hold true for arbitrarily large quantities? (similarly to mathematical induction)

I don't know what that word means.

I am a philosophical naturalist, but that is not taken on faith. Rather, by applying the scientific method to the available evidence, philosophical naturalism is an undeniable /conclusion/ (and like all scientific conclusions, it is tentative, and subject to being overturn with new evidence).

Try to explain sentience in terms of matter, then.

??
It's just the standard materialist position. I'm pretty sure you know it. The human brain is just physical machine, albeit vastly more complicated than most physical machines. Can we just skip ahead to your supposed "defeater" for my position?

Imagine an entity which is not sentient: for example, a rock*. Now imagine a human. Imagine taking the rock and making it more and more like a human physically. Do you believe that a point comes, at which the physical structure of your entity is at some particular stage of arrangement and/or complexity, when the entity suddenly becomes sentient? (Sentient as in "having a subjective experience") If so, can you conceive of what particular arrangement of matter is necessary in order to "activate" sentience? And where does the sentience come from? Why would it appear? Why are humans sentient rather than being so-called "philosophical zombies" that look and behave exactly as humans but have no subjective experience?

To be technical, there's no way to say whether it is a human body that is sentient or the entire universe that is sentient... but I'll talk about a rock to simplify things.

oops, the last sentence should start with an asterisk - it was supposed to be a footnote

(You) assume that the people who make these materialist arguments treat sentience as the equivalent of the soul, some magical different position for humans, when the logical viewpoint is that our perception of consciousness is simply how the machine that is a brain interprets information and makes decisions based on it.

>Do you believe that a point comes, at which the physical structure of your entity is at some particular stage of arrangement and/or complexity, when the entity suddenly becomes sentient?

I'm not sure. I suspect that as you continue this gradual process, one gets more and more subjective experience.

> And where does the sentience come from?

I don't know.

> Why would it appear?

I don't know.

> Why are humans sentient rather than being so-called "philosophical zombies" that look and behave exactly as humans but have no subjective experience?

I don't know if it's possible for p-zombies to exist. I suspect not, given the likely truth of the proposition that first-person experience is a result of a particular kind of physical configuration.

Regardless, this is a non-sequitir. I agree that these are interesting questions, but they do very little to nothing to address the massive wealth of evidence in favor of the Standard Model of particle physics, which leaves zero room for human souls except by very bad arguments like special pleading. To go from "I don't know", to "I don't know, and therefore there's a non-material magic soul that does it" is fallacious. It's textbook argument from ignorance.
tvtropes.org/pmwiki/pmwiki.php/Main/AWizardDidIt

What is the difference between a philosophical zombie and an actual human being?

philosophical zombies don't exist.

> one gets more and more subjective experience.
Remember the last time you woke up from sleep. Becoming sentient was binary, not gradual. You were completely not sentient, then you were sentient - only aware of a certain sluggish warmth, probably, not thoughts or visual stimuli (for the first second or so) - but already aware. Therefore I think sentience is binary. Either I am sentient or I am not.

regarding your latter point - it is irrelevant whether the SM leaves any room for souls. The key fact is that it does not exclude them.

By the way, I am only arguing about sentience, not about souls - I'm not trying to prove that souls exist, unless we just mean "sentience" by "soul".

Then it is logical to say that we live in a universe in which certain physical arrangements are correlated with subjective experience. I agree with that. However, then the question remains - why those particular arrangements and not others? What is the connection between a few pounds of neural tissue and qualia?