GOLDBACH CONJECTURE FINALLY PUT TO REST

But that's illegal, I wouldn't want to break the law.

cuck

>But that's illegal
so is killing yourself. In most countries anyways.

Only if they catch you.

>Given that the set of integers is infinite
nope, its capped at around 2^200

the only thing he proved is that he is a certified crank at this point.
I was still a bit in doubt about this guy. I mean constructivism sounds kind of cool and all. but he seems too far gone

>11 ways

I don't know why, but it makes me mad there aren't 12.

>the number of ways an even number can be represented as the sum of prime numbers is itself a prime number

Brb, PhD defense

I am a Wild fan but I don't feel too strong about this one. However, I like one thing. Finally Wild has put theorems where his mouth is. In the past he has only proved already proven theorems using his new famework so we couldn't really attack him. We already knew the truth of his result. But now, for the first time, he has gone out and resolved a problem that was yet unsolved in naive mathematics.

Is Wild right or wrong? We will now know. If someone is able to prove the goldbach conjecture true, going against Wild, then his theory is 0/10 crap or at least needs refining.

This is good for all of you, Wild haters. Dislike him? Just prove the Goldbach Conjecture to be true using your shitty infinite sets and then we will all have to shut up.

>inb4 new ZFC axiom: Goldbach conjecture is true

Like you solve all your problems, faggots.

You cant prove this just like you cant prove 0a = 0. So we must make this an axiom, dipshit.

It's a valid proof, just using a non-standard (and completely retarded) set of axioms. Wildberger basically takes the idea that there is no integer greater than 10^200 as an axiom, then uses that to show there are not an infinite number of primes, and hence not an infinite number of even numbers that can be expressed as the sum of two primes. His axioms are stupid and his proof is trivial, but it's logically coherent.

do you have to be autistic to care about math shit

>>the number of ways an even number can be represented as the sum of prime numbers is itself a prime number
oeis.org/A045917
fucking destroyed kid
3+7
5+5

thanks for the TLDR .... been slowly getting through his videos

where does the 10^200 integer limit come from ?

>new axiom: every number in that set is a prime number
BTFO
T
F
O

It's a rough approximation of the number of Planck cubes in the (visible?) universe. Since Wildberger thinks that's the upper limit on the number of things that can possibly be in the universe, he believes we can't say anything meaningful about numbers bigger than that.

Don't we have to consider the number of configurations of each of those cubes? Assuming we want to discuss probabilities of specific configurations...

On the chance that this question gets answered after I go to sleep.

Don't we have to consider the number of configurations of each of those cubes? Assuming we want to discuss probabilities of specific configurations.
Then don't we have to consider the number of maps between states? Assuming we want to discuss the relationships between cube configurations.
Then don't we have to consider the power set of the number of states? Assuming we want to talk about inverses of functional relationships between states in the general case.
Then don't we have to consider the number of maps between maps? Assuming we want to discuss the relationships between relationships between configurations in the general case.

And so on.

Not in his model. He only considers a number to exist if it can be represented by that number of things.
So we can show 2 exists by writing 2 = ||. 3 exists because we can write 3 = |||.
So, by that reasoning, the absolute biggest number is the number represented by all of the Planck cubes in the universe (which obviously assumes space is discrete, which I guess doesn't make his model any more retarded than it already is).
You can watch his videos explaining this on his youtube channel, njwildberger.

wait, is he using Z, used to represent the set of all real numbers, as a fucking variable?

what are you talking about?
[math] \mathbb{R} [/math] is the symbol for the set of real numbers

I thought he meant how R^3 = Z then tried to use it as a variable

what is he talking about then? some made up number z?

Everybody in this thread is now much dumber. ZZ is an extension to NN and NN is defined by the Peano Axiom. This trolls proof is shit. He is the flat earther of mathematicians.

what are you even trying to say?
peano axioms are weak shit for that matter, freshman tier.

BS. He broke the simplest rule for counting numbers. His proof is based on an non existing border.

again, what are you even trying to say? what are we counting here? the "proof" is retarded because the claim "there's no prime bigger than z" is silly as fuck, and nothing else.

This guy is such a retard

Why do you shill this meme?

omg! I just learned he is a math prof. He must have a accident with severe brain injuries. Is it enough to count cows to five to become a math prof in australia? Or are there some magic rules for prime number frequencies down under flat earth.

2 is prime

A) Magic is called Betrands postulate.

B) Disprove of a conjecture by a missing proof is BS.

It is like:

> 100 german scientist against Albert Einstein.

I hate it if science is replaced by propaganda. Australia is lost.

3+3+3+1

As far as I understand it he assumes there is a finite number of integers with z being the largest

Ridiculous...

False proof and awful exemples.

ITT angry brainlets who can't into finitism

z is 10 triangle 10 + 23

Wild has over analyzed the properties of this specific number over his last 10 videos or something.

ayyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

But you just wrote it famalam

We already know there are infinitely many naturals and primes, so there's no way he can be right

He defines numbers as lines on whiteboard, and because there are finitely many whiteboards in the observable universe there are finitely many naturals, and their number is estimated to 10^200

So something as easy to write as 10^300 doesn't count, then?

I really think his stuff is more foundational digital physics, and less math.

>So something as easy to write as 10^300 doesn't count, then?

Actually no and Wild has a very good reason for why.

You and I think that a number by any other name is just as rigorous, right? Well, Papa Wild doesn't think about it. Papa Wild thinks of natural numbers in 3 different ways

Primitive natural numbers: his msets where, for example, [I I I] represents the number 3.

Hindu arabic numerals: Where you take the idea of primitive numbers and assign symbols to a number of them and then construct numbers using these symbols.

These allow us to create more numbers. For example, the biggest hindu arabic numeral is 10^10^200, not 10^200.

This is good for theoretically thinking about dark numbers (there are no dark primitive naturals) and to more orderly think about normal numbers (writing 10 is way better than writing [IIIIIIIIII])

Then there is Exp, the set of expressions. In this set lie objects like 5+5 which can be shown to be equivalent, but not really the same, as 10.

Exp is a really weird set, and something like 10^300 belongs to this set. One of the main differents between Nat and Exp is as such:

If I gave you two primitive naturals then it would be TRIVIAL to tell which one is bigger. The one that is longer, obviously. But what if I gave you two arbitrary members of Exp? There are cases where you would have no idea. For example

What is bigger

10^30^2^300 or 10^32^3^299

Maybe if you know a couple of tricks you could, but if I gave you an even bigger tower of exponentials. At one point there would be no way to know because what if your expression translates to a dark number,

10^300 is a dark number so if I ask you to prove me that 10^301 is larger than 10^300 by giving me the mset that this expression represents, you could not do it. There is not enough space in the universe to represent a dark number such as 10^300 or 10^301.

That is why simply writing "10^300" doesn't count. Expressions behave very differently from naturals.

this is equivalent to the goldbach conjecture you idiot

There are lots of m-sets you couldn't give me. You couldn't even draw me the m-set for 4 trillion; you'd die before you had enough time to finish drawing lines.

"Space in the universe" is a completely arbitrary constraint; when you get to the point where you're saying "theoretically it COULD be written down, if you had access to a ridiculously tiny marker and could write 1000 lines a second and had a trillion years and access to all the space in the universe" why not just add one more theoretical quantifier that you won't run out of space

>There are lots of m-sets you couldn't give me. You couldn't even draw me the m-set for 4 trillion; you'd die before you had enough time to finish drawing lines.

But I theoretically could give it to you, because 4 trillion is not a dark number. There is enough space in the universe for me to do it.

>"Space in the universe" is a completely arbitrary constraint; when you get to the point where you're saying "theoretically it COULD be written down, if you had access to a ridiculously tiny marker and could write 1000 lines a second and had a trillion years and access to all the space in the universe" why not just add one more theoretical quantifier that you won't run out of space

Because saying there is a limit is more sensible than pretending there isn't.

Does Wildberger literally believe that Planck cubes are the smallest volumes possible in the universe? Is that what he bases his finitism on?

>Because saying there is a limit is more sensible than pretending there isn't.
Why?

But it's sensible to assume that not being able to write it down before the death of the sun _isn't_ a limit?

It is a part of his theory but it is not fundamental. When he talks about numbers he either talks about small, normal, numbers or really big numbers that go way beyond 10^200 to show why they are not nice.

He never ever tries to talk about numbers really close to that 10^200 boundary because even 10^200 is arbitrary. If tomorrow we had better measurements about what is the smallest unit of space then we would recalculate the biggest numbers based on that and nothing else about his theory would change.

Because then you get batshit crazy statements like "the square root of 2 exists" to be true in your framework.

It is a limit but it is way different from being literally unable to write it down, regardless of how much you may try.

Also, remember that non-dark numbers have really nice properties. Most important is that low complexity non-dark numbers are very easy to compute on. One trillion (1,000,000,000,000) may look big but to a computer it is nothing.

We can very easily do mathematics with one trillion, even if writing down its mset would be long, it is enough for mathematicians to prove that it is not dark to be able to do useful calculations with it.

>the square root of 2 exists
Why is that crazy?

If I draw two lines of unit length, each connected to the other at one end at a right angle, what is the distance between the other two ends?

>It is a limit but it is way different from being literally unable to write it down, regardless of how much you may try.
lmao

because if you try hard enough you can fill up every planck cube in the universe with a tiny little line

His choice of ceiling is as arbitrary as any other and the only reason he chose that one is that it's the least bullshit sounding he could find.

Please just watch Wild trig to understand this. I will just say that the only thing the pythagoras theorem says is that

c^2 = a^2 + b^2

Any other conclusion you want to get from this, like maybe taking the "square root" of both sides is unsubstantiated, unrigorous garbage that comes from a mindset that takes arithmetic for granted.

Saying that something equals c^2 implies that c has to at least exist. You can't square something that has no meaning.

>Saying that something equals c^2 implies that c has to at least exist.

That is a very nice claim... prove it.

You think it does because you have been taught to think of the fundamental metric as length... but it isn't. The fundamental metric is area.

c^2 on its own represents something geometric, a square, and this is well founded.

And sure, c would be technically the length of this square but this doesn't mean that c has to be a traditional number. Papa Wild argues for a complete algebraic treatment of irrationals that occur naturally in geometry. Where we simply say that root 2 is the number that satisfies the equation x^2 = 2 without asking anything more about it because if we keep pushing for the "truth" then we start thinking about infinite decimals and there is no such thing as infinite.

But also, as Papa Wild does, we should avoid these algebraic constants as much as we can. Even if rigorously defined as algebaic identities, they are still a very weak foundation. That is why he thinks of a theory of spreads (ratios of areas) instead of angles (ratios of lenghts) and area as the fundamental metric instead of length. This way the weird constants would just arise in the algebraic context, where it makes much sense to use them as our crutches to find results.

>occur naturally in geometry
Why is nature a concern when constructing abstract number systems?

>That is a very nice claim... prove it.
>Where we simply say that root 2 is the number that satisfies the equation x^2 = 2
well you literally just told me root 2 exists so it doesn't seem that I have to.

>well you literally just told me root 2 exists so it doesn't seem that I have to.

The algebraic notion presented here by Papa Wild is nowhere as flawed as the analytical notion of irrationals, typically represented by infinite decimals, or cauchy sequences (which are infinite sets).

Why are they flawed? Because of infinities?

How do you know infinities don't exist? (Reminder: we have no reason to believe that space is not infinitely divisible)

Also what is the angle between two perpendicular lines, in radians?

but I never made any claim anywhere about infinite decimals. I simply said irrationals exist after you claimed that root 2 existing was silly; I never said anything about it meaning you can represent them as infinite sets.

you're regurgitating nonsensical rhetoric that you don't even understand so you keep going back to irrelevant points

probably trolling but it's funny so it's fine

radians are defined by the illogical pseudo-mathematical notion of a "circle"

There's a much bigger problem here.

Even if sqrt(2) exists, that doesn't mean that all reals exist. In order to prove the existence of a real you must demonstrate it and given that our language only allows a countable number of definitions then it is provably impossible to demonstrate each real number. At best we only have a countable subset which happens to be a superset of the algebraic numbers but a proper subset of the reals.

no you do not know that the number you get is sqrt2, because a number is just an assignment to a length. there is a length, since you can lay down your ruler on the line, but you do not know if it is possible to give the length the number sqrt2.
you think that it is possible only because you assigned previously natural numbers to lengths

Same thing for assigning a volume, a mass to anything.

>I can give you m set of 4 trillion because it's not a dark number, and it's not a dark number because I can give you it's m set
Well that's stupid as hell mate.
Also, his reasoning on upper bound of naturals is retarded as hell, he says you can't have number greater than 10^200 because there are no more plank cubes, so it's impossible to construct such number, but he fails to notice it's practically impossible to construct number 10^200, 10^200-1, 10^150. They are as impossible to construct as 10^200 or bigger numbers and yet wildburger has no problem with calling them naturals and admitting they exist

Isn't number system basing on arbitrarily bounds useless? If today 10^200 is the biggest number but tomorrow when more whiteboards are discovered 10^202 becomes new bigger number, why even bother with such shit structure?

If we say one plank cube represents number 10^200 instead of one (because both assumptions are both arbitrary) then the biggest number possible is (10^200)^(10^200)

If c*c exist then would it have any sense to say c*c exists while c doesn't?

Then how do you explain a book that has all the numbers of the largest mersenne prime

This is a grod post. +1

Please watch that one wildburger's video when he was solving problem using rational geometry and quadrances, which are supposed to get us rid of irrationals, and the answer he got involved sqrt of 6

Cult of abstraction is garbage

We don't have to prove existence of each and every real, same as wildburger never proved the existence of all naturals from 1 up to 10^200.

Is this guy retarded? I didnt understand a word he says. He is supposed to be intelligent, why cant he explain his theory to me? IS he RETARDED?

I actually like the "proof".
The mathematics he practices is quite different to what is standard today and while what he is doing might not do any good it at least gives a new perspective.

The "proof" is a consequence of his ultrafinitism and while the complete point of the problem was missed it also demonstrates the relation between mathematics and the real world.

For a pure mathematician his theories are probably a waste of time because actively limiting oneself is a bad idea.
But for CS or Engineering some of his stuff might even be useful and a lot easier to comprehend for students.

I could even imagine that his "rational geometry" might have useful applications in engineering where solving a trigonometric problem requires calculating trigonometric function to a high degree of accuracy.

I am completely stupid and I understand him so I imagine it is your fault.

How is , "the set of points equidistant from a given centre point" illogical

How are "object of no size" and "finite, non zero object made of infinitely many objects of zero size" logical?

I'm not talking about a physical object, I'm talking about locations in a space

You are retarded 2 is a prime number.

1 ain't prime

Another cringe thread /b/?

So how can he be sure that the number 1 trillion exists, seeing as noone has ever put that many strokes on a board?

Locations of what? Of sizeless, (that is nonexistent) objects?