How does he even explain what a circle is without reals

How does he even explain what a circle is without reals

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If I asked Wildberger what the zeroes to x^2 - 2 = 0 are what would he say?

>You mean the fundamental dream of algebra?

Or something like that.

What's his goal

To have well defined objects that you can write down on paper.
youtube.com/watch?v=E_dGqavx5AU
or
youtube.com/watch?v=WabHm1QWVCA

youtube.com/watch?v=bmEM75lTLes

youtube.com/watch?v=xp0H3Aw0j6E

Shill his ``revolutionary'' theory of Rational Trigonometry.

it has an approximate solution x=1.4142

ît's a meta-number, something beyond the grasp of our brainlet minds

He doesn't have a problem with reals, just their construction.

>there are plenty of mathematician that would agree with him

Lol

but what about [math]e

fuck this retarded guy

His mind can only work on discrete mode?

Yes, just like all of ours.

I see.

I suppose what counts as "well-defined" or "poorly-defined" is subjective, but I objectively can write an infinite set on a piece of paper.

Post it, and be sure to show every element of the set.

So to him a set is invalid if each element cannot be simultaneously written?

Pretty much. He also denies the existence of numbers that are too large to be represented. It's similar to constructivism, though he doesn't call it that.

>A finite set with a quantity of elements equal to Graham's number doesnt exist because you cant write all of the elements.

rly made me think

>How does he even explain what a circle is without reals

Ah, please tell me, brainlet. How does it feel to be retarded? For all my life I've never been retarded and now I feel curious.

Anyways, you don't need real numbers to define circles. In fact, you don't need any numbers to do geometry because geometry is completely independent from arithmetic and the only reason that nowadays we mix up arithmetic and geometry is because of something a little brainlet like you is too dumb to understand so I'll skip that part.

If you want to define a circle properly then you can follow Euclid's reasoning. A good way to put it in modern terms is:

Given a point P and a segment S such that one of its endpoints is P. Consider the set of all the segments that have P as one of its endpoints and are congruent to S. And consider the set of all the endpoints of these segments that are not P. That set is a circle.

Where did I use numbers? Nowhere.

>b-but you are just saying the points are equidistant, which implies distance! Which means real numbers

Now you retarded baboon. Distance only comes into play in geometry when you define a metric inside a subset of euclidean space and geometry does not give two fucks about which metric you apply to it. In fact, it doesn't give a fuck about you applying a metric at all. Metrics are a brainlet crutch we use today so that brainlets can also do geometry problems.

Now back to trade school Tom, your brain is too small to comprehend Norman's genius.

Like this :)

Wildberger would prefer to treat the square root of two algebraically or as approximations. He's indicated in several videos that even though it "looks like" a line might intersect a circle, it doesn't if the hypothetical point of intersection doesn't exist in the rational parameterization of the circle.

I'm not sure why this makes people so butthurt.

i feel like he's not talking, he's talking to people in 2100 that will discover his work after his death like galois was

to us*
FUCK i made a mistake. SHIT

I seriously doubt he thinks like that. He's definitely talking to us.

You weren't kidding

njwildberger.com/2015/11/19/the-fundamental-dream-of-algebra/

Wouldn't this mean that the parameter of a circle is 4 times the diameter? It looks like taxicab geometry

Doesn't he have a video on exactly this topic?

rational trig is valid over a finite field, can be completely accurately computed in polynomial time, extends naturally to spherical and hyperbolic geometry, and is easier to teach to kids.

Im not so sure youve really internalized any of wildbergers arguments.

Things liek points, lines, and circles are defined algebriacally, and therefore point on a line circle can be tested for the property that they in fact reside on the circle.

Wildberger talks quite a bit about how geometry is subservient to arithmetic, that part of his whole orientation that guides rational trigonometry.

Cantor still triggering brainlets 150 years later

>He also denies the existence of numbers that are too large to be represented

This is patently asinine. Why is a power tower not a legitimate representation? Because the True way to write a number is left to right, as the sum of products in our chosen base system?

Why not take every letter and number from every known alphabet and form a base 10,000 system! Thus we have made manifest numbers that literally never existed before!

>Hey guys, Roman Numerals suck, check out these neato Hindu-Arabic numbers
>>Yeah nah get fucked
Years later:
>>He was right...

Same with Norm. Watch his Foundations of Mathematics playlist from video 1 (What are numbers?) and he lays it all out.

His position on these things is roughly along the lines: if it is a "number" you can do "arithmetic" with it in such a way that is not merely restating the question.

It goes against their sophomoric learnings. Norm handles sqrt(2) just fine. Like you say, treat it as a mathematical object in and of itself without trying to transform it into decimal notation, or approximate it as a carpenter would. Both are valid depending on who you are and what you're doing.

Veeky Forums hates Wilderberger because they know he's right

that we can't define it and it's not normal object that can be defined, but rather meta object, meaning circle is whatever norman says

He's /ourguy/

>Because they wouldn't be real numbers if they were defined differently
but reals are already defined in couple different ways, axiomatically, as totally ordered complete field containing rationals as subfield, as Dedekind cuts, equivalence classes of Cauchy series of rationals, as field extension of rationals. There's no problem in defining an object in many different ways as long as the definitions are equivalent. And that may be the problem for wildburger, if somebody provides definition of reals that he will like then either it would be equivalent to other definitions of reals, meaning wildberger can't accept it, or it isn't, but then in defines object different to reals

>reals are already defined axiomatically
imagining you can imagine things

BTFO

Indeed

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?

why is this wrong? what is the loophole?

Stop namefagging and i'll tell yah cully

this doesn't approximate arc length it approximates area

If you unironically can't come up with an intuitive explanation as to why this is wrong on your own, you're 100% a brainlet

Maybe he'd give the standard Algebrautist's answer... "x^2 - 2 = 0 *is* the square root of 2!!"

The point is even though some large numbers are representable through extended notation, there are many more numbers of similar magnitude which could not be represented. This is true for whichever set of symbols or short-hands are used.

Quick explanation:

it is not always the case that the length of a limit of continous function sequence is the same as the limit of lengths of continous function sequence.

If you look at the sequence of edgy curves in the pic, there is, for each point on the circle, a quantity which goes towards 0: the distance from that point to some point on the curve, which the outgoing radial line meets.

Remark: Limits of sequences are always defined with respect to a norm (which ironically is related to Wildbergers problems)
For example, the statement
[math] \lim_{N\to \infty} \sum_{n=1}^N \dfrac{1}{n^2} = \dfrac{\pi^2}{6} [/math]
So there, the sequence of rational numbers 1, 1/4, 1/9, 1/16,... has an irrational (transcendental even!) number as limit, and this is with respect to metric distance on the real number line, that's always used for infinite sums and so on.
Assuming you defined pi somehow else, this is an identity that can be proven in analysis. Worth pointing out that in many contexts, real numbers are defined as limits (of equivalence classes of) sequences of rationals in the first space.

Now all distances between the circle points and the curves in the sequences becoming smaller as you go further in the sequence
is just the wrong choice. (if you want the perimeter not to be 4)

For example, the curves in the sequence also have bad differentiability properties. Not that this alone would be a strong argument - pi sqared also has "bad rationality properties" :)

pic related

The space for which Z is the homotopy group, i.e. the type S with terms
base : S
loop : (S=S)
where (X=Y) is a space of paths from X to Y, generating the integers as [math] n \sim \text{loop}^n[/math]

Limits of sequences are always defined with respect to a norm (which ironically is related to Wildbergers problems)
For example, consider the statement
[math] \lim_{N\to \infty} \sum_{n=1}^N \dfrac{1}{n^2} = \dfrac{\pi^2}{6} [/math]
According to this, the sequence of rational numbers
1,
1+1/4,
1+1/4+1/9,
1+1/4+1/9 +1/16
...
has an irrational (transcendental even!) number as limit.
Assuming you defined pi somehow else, this is an identity that can be proven in analysis.
And this is with respect to metric distance on the real number line (which is always used for infinite sums in analysis).
(Worth pointing out that in many contexts, real numbers are defined as limits (of equivalence classes of) sequences of rationals in the first space.)

If you look at the sequence of edgy curves in the pic, there is, for each point on the circle, a quantity which goes towards 0:
The distance from that circle point to some point on the edge curve, which the outgoing radial line meets.
All distances between the circle points and the curves in the sequences becoming smaller as you go further in the sequence
- but this is just the wrong choice for a limit if you want the result to be identifiable with the circle embedded in R^2 like you're used to (i.e. if you want the perimeter not to be 4)

Btw., note that also all the curves in the sequence also have bad differentiability properties. (Not that this alone would be a strong argument. Pi squared also has "bad rationality properties" :)

pic related

The space for which Z is the homotopy group, i.e. the type S with terms
base : S
loop : (base=base)
where (X=Y) is a space of paths from X to Y, generating the integers as [math] n \sim \text{loop}^n[/math]
(sorry, fixed error)

Fuck all the haters.
I can't wait for his algebraic calculus course.
It will revolutionize math.

I'd respect Wildberger's goals if they were to construct rational mathematics as a simple, highly rigorous alternative to real mathematics. But any time I find myself starting to like him he turns around whips out a hundred tonnes of intuitionist bullshit out of his ass, like there being a largest natural number and so on. If you're just going to make shit up without bothering to justify it, why even call what you're doing "mathematics"?

Because the definition of the length of a paramteric curve defined by f is:
[math]\int_{a}^{b}|{f}'(t)|dt[/math]
Notice that f does not come up in the formula, only f'.
The "troll" curve converge toward f that is true, but it's derivative does not converge toward f'.
This is actually some moderately advanced math and you can bet nearly no one on Veeky Forums gets it, especially the one who mocked you. (most of them probably think the troll curve doesn't converge toward f)

This formula also explain why translation doesn't change length too.

why did I fail my latex?
[math] \int_{a}^{b}|{f}'(t)|dt [/math]
[math] \int_{a}^{b}|{f}'(t)|dt [\math]
[eqn] \int_{a}^{b}|{f}'(t)|dt [/eqn]
[eqn] \int_{a}^{b}|{f}'(t)|dt [\eqn]

here is the formula I failed:
[math] \int_{a}^{b}|{f}'(t)|dt [/math]

I think wildburger has confused math, a human construction, for something that inherently exists.

I hope Stephane ended it that night.

I think most "modern" mathematicians confused math (a tool) for some philosophical language.

>Why is a power tower not a legitimate representation?
Brainlet detected. Nothing I said implies it isn't, and in fact he has a sequence of like 6 videos explaining fast-growing hierarchies that can produce impractically large numbers.

If one of the definitions has a problem, then equivalent definitions are going to have similar problems.

He already has some videos explaining derivatives and integrals algebraically. He doesn't offer anything particularly new, but I do like his compact way of writing polynomials

youtube.com/watch?v=vyRFz8J4Y_M

youtube.com/watch?v=vo-ItaB28f8

Somebody invite him here to discuss already. I'm sure he's the most competent guy to defend his reasoning and since he's sharing all these videos on youtbe, he seems to be willing to answer some questions about his work online.

If you have a question for him, you can ask him in his comments sections. Asking him to post on Veeky Forums is stupid.

No, that is why I said I wouldn't get into why we introduce numbers into geometry because your brain was too small.

All I claim in my post is that geometry is completely independent from number systems and therefore anyone can talk about geometry. Even if you don't even believe in natural numbers you can talk about geometry.

But the reason we introduced numbers was because it makes the theory very rich. When you introduce metrics (Wildberger's quadrance and spread are a kind of non-standard metric) you can first find that there are many statements about congruence that directly translate into statements about metrics. Thus you can create a quick algebra-geometry relation which is why techniques like Bashing are taught to students. The argument Wildberger brings to the table is how this algebra-geometry relation should be handled. How should it be actually defined. If you do define it in the lazy way then you quickly find that irrational numbers appear so you immediately did something wrong, so Wildberger is trying to find the right way to define metrics on geometric spaces.

>If you unironically can't come up with an intuitive explanation as to why this is wrong on your own, you're 100% a brainlet
Let's hear it then. I'm waiting.

The irony being that Wilderberger's problem with infinite sets is a philosophical one

If this object was equivalent to a circle, the derivative of a circle would be 0 or undefined at every point on its circumference

lol

I think Wildberger makes a mistake when calling his mathematics non-philosophical, as that itself is a philosophical position. You ultimately can't avoid philosophy (or meta-mathematics ftm).