Do you still think you can count past 1000^10^200?

>>8353631
>Planck cubes

There is no evidence that spacetime is discrete. It completely breaks both general and special relativity. Therefore plank units are just an arbitrary choice of units that make calculations look nice.

>>8353631
What a load of bullshit.

>>8353638
>>8353648
this desu

>>8353638
>>8353648
brainlets who can't understand dark numbers.

>>8353631
Let x be the largest number that can be written down. Then x+1 is a number that is written down

B T F O

T

F

O

>>8353631
You can in principle and that is all that matters

>>8353631
>pls let me be in math textbooks

>>8353638
>no evidence spacetime is discrete
Quantum physics would like a word with you.

>>8353660
prove that x+1 exists.

>>8353682
Quantum mechanics does not imply spacetime is discrete. This is especially obvious since we already have QFT.

>>8353682
maybe you should read up on qm before you post about it.

>>8353687
Let X be defined by the Set of Writable Integers, and Y be defined by the Set of Unwritable Integers. X U Y = The set of Integers (Z), therefore Y exists as both X and Z exists

>>8353687
as per Wildberger's definition, a "number" is a series of marks on a piece of paper. such a number can be represented in shorthand notation by substituting all occurrences of it with a letter, such as "x". In this way, the number is written down without explicit reference to its original definition. now,define the operator +1 as the action of adding an additional mark to a number. via the process of abstraction described earlier, where a number is schematically represented as a single character, we can make sense of expressions such as "x+1" as "the number which we would obtain by adding an additional mark to x, assuming that we had sufficient physical space to do so"

>>8353705
you still haven't shown you can add an additional mark to an arbitrary number.
>>8353694
get out of here normie

>>8353694
the problem is that you posited that X and Y exists and you have not proven anything

>>8353710
>>8353720
Brainlet that cant admit defeat detected

Let X be defined by the Set of Writable Integers

By definition the complement of X is the set of Unwritable Integers (Y)

Both the Set of Unwritable and Writable integers will equal The set of Integers by definition

As per the fucktard in the OP you define """"dark"""" numbers by something we cannot write IE those present in the set of Y
IE in the notation of p->q
p: I cannot write down a symbol to represent an integer (Z)
q: It will be in the complement of X


Proof:
Let f = 1 and g = 2 -> 1 + 2 = 3 = f + g, therefore by the properties of substitution I can use a mathematically equivalent expression to substitutive for another

Let W equal the sum of the set of Integers from one integer (k) to another(h)

ex 1. let k equal 1 and h equal 100, thus the sum of the set (W) = 5050,
ex 2. let k equal 1 and h equal 1, thus the sum of the set (W) = 1
Thus by the properties of positive whole numbers we can always assume F to be always be greater than or equal to h

Let k equal 0 and h equal the same infinity that bounds the set of integers, then the sum of the set equals (W) = aleph null, or infinity

By the definition of infinity provided in grand hotel problem -> W + 1 = W

By the definition of equality if W exists (and I just proved it did) then W+1 must also exist too and for the man in the OP; W can be used to denote any number larger to or equal to ANY integer so by mathematical Induction the set of W complement is null and as such the duality of p->q is satisfied.

>>8353778
I think perhaps you're not understanding the rules of Wildberger's Wacky World here.

There is a very simple "proof" that there is a largest number.

1. The universe has a finite lifetime
2. Therefore, there are only a finite quantity of numbers which humanity will ever explicitly construct, write down, or otherwise derive a value for. These are the only numbers that will ever, in any meaningful sense, exist. All other numbers, which will never have a value that anyone could actually express, are bullshit made-up numbers.
3. Of these numbers, one will be larger than or equal to all others, because any finite set of finite numbers will have one or more largest elements.

Therefore, there exists a largest finite number.

>>8353682
Shut up you brainlet

>>8354318
the guy just wants to have a second of fame. through symbolism you can define all real and rational numbers

>>8354372
Given that there are uncountably many reals, but only countably many symbol strings, I must disagree. You can describe the *set* of reals through symbolism, but you cannot describe any particular arbitrary >>8354333
real.

ive just finished wildtrig, thought it was great. You guys really hate him, for what, math foundations stuff? Im not that far yet?

>>8353631
> read the poster badly
> read "dank numbers"
> thought to myself "born too soon..."

>>8353665
He has already written math textbooks.

>>8354423
He's great. and he shills for ultrafinitism. Which, depending on your views, might make him greater, or not.

>>8353631
Where do /sci/ find these crackpot scienetists?

>>8354318
Can you express the exact value of pi? You cannot, because its decimal development is infinite and non-periodic.

A number is nothing but a collection of digits. The place where the comma (that marks the digits counting units) makes the "size" of it

1,23456 < 123456
but those are the same collection of digits

If you're able to construct an infinite collection of digits (we have it with pi for instance), you can arbitrarily construct as big a number as you wish by moving the comma towards the right.

You're mixing set with a boundary and finite set. It's all mixed up in your mind, but I appreciate your effort for discussion and clearing things up.

>>8353631
>1000^10^200+1 exists

proove it. write it down for me if it exists.

>>8354560
you just wrote it down

>>8353631
1000^10^200

+1

>>8354560
>>8353631
>brainlets think there is any reason to favor the base 10 expression of a natural over any other notation

>>8354560
Easy. It's 10 in base 1000^10^200+1

how do I get smart like him

>>8355877
step 1: replace radians with spread values
step 2: replace trigonometric functions with spread functions
step 3: do trigonometry

there's no real advantage to rational trigonometry over trigonometry with pi

if wildberger was onto something he would have already solved the abc conjecture

>>8353631
Stuff like that just makes him look like he is actually retarded.

>Planck cubes has some sort of quantization of space aka popsci garbage
>The physical representation of numbers is absolutely meaningless and arbitrary.
>The importance of mathematics and abstract thinking in general precisely IS that those abstract objects do not need to be represented physically in order to work with them.

>>8353638
Is it possible that it's similar to wave particle duality? ie when you look at space being discrete then time behaves continuously, and when you look at space being continuous then time behaves discretely? And then likewise if you're looking at time?

I know im fucking retarded but im a drunk cheme guy so i am asking even though i know it's a load of shit question

>>8355901
No. There's simply zero evidence that space or time is in any way discrete.

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>>8353631
>1000^10^200 + 1

>>8354447
>study set theory
>define the dank cardinals, meme cardinals, datboi cardinals, Pepe cardinals
>get PhD in math
>proove you were born at just the right time

base 100

now what?

>>8355904
>that fucking passage in the Feynman lectures where he goes
>"you have to make specific claims. Not just "space is discrete", but something specific like "space is discretized as a cubic grid along three axis". Then if you make that specific claim we can immediately prove it's wrong. It doesn't work, it gives the wrong predictions."

This shit haunts me. I have no idea how you can prove that. Was it a "Fermat's theorem" case where he thought he had the proof but didn't? Or is it really that simple?

>>8353638
>>8355895
He should use the Bekenstein bound meme instead of the Planck distance meme.

>>8356030
It would have to be more specific than that to be falsifiable. If for example, you wrote down a discretized version of Maxwell's equations, the simplest versions you could write down would make the speed of light slightly dependent on direction, and you could test for that. But you could also write down a more complicated version of Maxwell's equations that would reduce the anisotropy. And even given a specific theory, you would probably only be able to set an upper bound on the size of the cubes.

where does the 1000 come from?

>>8353631
>Do you still think you can count past 1000^10^200?
1000^10^200+1

BTFO

>>8355892
>there's no real advantage to rational trigonometry over trigonometry with pi
Rational trigonometry can be simulated with transcendental trigonometry by just using squared sine, squared cosine, squared tangent, etc. The difference between the two is that rational trigonometry is set up to work in arbitrary fields (though not usually fields of characteristic two) and transcendental trigonometry is not.

Whether this proves any long-term advantage, I don't know.

>>8353631
>>8353659
I am under the impression that this video is satire making fun of physics?

>>8354318
I really hope this is bait because if you don't realize how dumb that position is I wonder if you ever made through elementary school

>>8353687
>>8353710
It's an axiom you retarded mongrel brainlet faggot.

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>dark numbers
HOLY FUCKING SHIT I CANT, MY SIDES ARE IN ORBIT

>>8356378
It's making fun of mathematicians who need to invent "dark numbers" to plug holes in their theory.

>>8353687
Let x be a number such that x > x - 1 for all x in the set of real numbers. This clearly implies that x + 1 > x.
Let's prove the first statement by induction.
Our base case will use x = 1. 1 > (1 - 1) which is equivalent to 1 > 0, which checks out. Base case is right.
Now for case (x + 1).
(x + 1) > (x + 1) - 1 is equal to x + 1 > x. As we saw in the initial statement of the question, x > x - 1 and x + 1 > x, so it checks out.

>>8356849
prove that the induction is a valid rule of inference in whatever formal system you choose to work in, then tell why you choose to work in this formal system and not in another one, where possibly you do not have indction. protip you kant

>>8353631
a priori vs a posteriori

If you're going to talk about what you can go outside and count, of course they're are going to be limitations.

If you're being purely mathematical then the size of the universe is independent to the number system.

>>8358096
>If you're being purely mathematical then the size of the universe is independent to the number system.
but then it is autism

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>>8354478
>comma

biunp

>>8353638
Whether spacetime is discrete or not is not the issue, you can never measure the position of a particles more precisely than 1 Plank unit.

>>8360348
So?

>>8360348
That's only according to some quantum gravity models, it's not a substantiated claim.

>>8358096
>If you're being purely mathematical then the size of the universe is independent

The number system is an idea. An idea is inside a mind. A mind is made out of matter, therefore an idea is made out of matter, therefore numbers are made our of matter.
The universe is discrete and matter is finite therefore numbers are finite.

Why is everyone in here too stupid to understand this? Its basic logic.

>>8360561
>What is abstract thought

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Hey everyone. Quantum physics is bullshit.
It is only for computation. Has nothing to do with how reality works.
It's a tool. Not a model of the universe.

>>8360561
>An idea is inside a mind

aaaaand thats where you went wrong

>>8360561
You're confusing the map for the territory. A song is contained in a CD, or in waves in air, but we can still talk about a song that would go on forever. The song itself is not the medium simply because it is made up of or represented by the medium. It's an abstraction.

>>8360561
>The universe is discrete

so you're just ignoring that all contemporary physics requires the universe to be a differentiable manifold?

>matter is finite

conjecture

> therefore numbers are finite

does not follow

>>8353682
>that's what someone who has never learned anything about QM besides what is in popsci documentaries believes

>>8360596
welcome to science, now fuck off back to where you came from

>>8354318
(that number)+1

what now normie?

>>8360629
>so you're just ignoring that all contemporary physics requires the universe to be a differentiable manifold?
doesn't say much about the discreteness of the universe. Being able to model the universe as continuous is computationally beneficial and reasonable to a certain degree of accuracy but not necessarily fact.

Why can't I define infinite numbers within the space between planck space? Why is the universe so fucking gay?

>>8362012
Once upon a time you could just say "the map is not the territory" and people would understand their category errors, but it seems that time has passed.

>>8353631
Literally nobody has ever counted past 100

>>8353638
What's wrong with making up artifical units to make calculations look nice if the result stays the same?

>>8360561
My God kys philosophag

>>8354318

tell me what is the physical representation of sqrt(-1) u filthy faggot. now go listen to the teacher teaching.

>>8355942

I honestly think at one point there'll be papers published with meme reference in it, and people centuries later will have to use it,

>>8353682
HE ACTUALLY FELL FOR IT THE ABSOLUTE MADMAN

>>8358721
what is it you've eaten scumfag?

>>8363084
The point (0,1) in Rat^2 given complex structure, dimwit

>>8353631
Last time he said 10^200 was the biggest number possible, now it grew to 1000^10^200? How, did the number of whiteboards in the observable universe grow?

>>8353710
It's easy to prove that for any real x x+1 exists and is real, but in wildburger's system it's impossible to prove because he keeps making up silly rules

>>8353631
>count past 1000^10^200
1000^10^200 + 1
EZ PZ fgt

>>8353778
wp

>>8363514
In general Wildberger cannot rely on the rationals forming a field, since he cannot rely on the product of any two naturals or integers existing and such products are required to determine equality of rational numbers. This has always been the problem with finitism from a foundational perspective. I think this is why he is enamored with the idea of "types." Then something like a product of two integers is either an integer or never halts (in our lifetimes). So you can picture that the field axioms become something like proofs about types where there are bottom types littered throughout everything because some operations may never halt (in our lifetime).

>>8354447
read this, reddit.fuckoff

>>8353631
1,e6000

>>8354560
literally not knowing what windows calculator is

>>8356392
No it isn't... It is however trivial by induction

>>8353631
1000^10^200 and one.

>>8353631
How does he count the pairs of existing planck cubes?

so what happens if I write down this number and then add one more 0 at the end

>>8353660
If there is no largest number that can be written down there can be numbers that cannot be written down.

>>8356241
>Bekenstain

FTFY

>>8368552
In particular by the well ordering principle there is a smallest number that is too large to write down.

>>8356382
It's supposed to be silly. Ultrafinitism, and Wildberger in particular, is very silly. That's my point.

But "there is a largest finite number" is such a ridiculous statement that people have a hard time understanding how anyone could possibly say that. I was trying to illustrate the sort of mindset behind Wildberger's Wacky World, which is that mathematical induction cannot be assumed and you can't trust that any number exists until you explicitly construct its value.

>>8353631
Yes. I'll just start at 1000^10^200 and start adding 1.

1000^10^200
1000^10^200 + 1
1000^10^200 + 2
...

>>8368570
The smallest number that cannot be written down does not exist, because if it exists I just wrote it down in the beginning of this sentence.

>>8354560
>Number exists iff it can be easily represented on one, arbitrarily chosen notation

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he destroys math in one slide

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>>8369308

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>>8369313

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>>8369326
this is what is coming. math is rekt

>>8354478
>Can you express the exact value of pi? You cannot, because its decimal development is infinite and non-periodic.
pretty sure I can do it in base pi.

10

idk can wolfram alpha do it

>>8353631
They're called BBC numbers actually.

>>8369326
Who cult of complexity here?

>>8353687
Because [math]x-1[/math] and [math]x[/math] exist, so does [math]x+1[/math].

>>8353631
> it's THIS thread again
C'mon, this is beyond reality.

Must be... Hyperreality eheheheh

>>8362953
underrated post

>>8369308
>Define naturals as strokes on a whiteboard
>Complain about lack of rigour in modern maths

>>8369348
What's maxel?

>>8363084
The physical representation of sqrt(-1) are the bits or atoms that are needed to store its representation.

If we give a physical representation to every number then there are only as many numbers as there are physical things.

Every other number doesnt have a physical representation and therefore it can not exist.

Lets assume we can compress the information a number carries as often as we want (and therefor maybe generate infinitly many numbers) then, according to shannon, "a compressed message has less redundancy".
The limit to this is the point where there is no redundancy at all, this means at best every number has exactly one representation. If the universe is finite then there is a maximum amount of numbers which is possible. If it grows then its generating new numbers.

But if its infinitly big (and small) then there cant be a unique representation and shannon was wrong because less redundancy on one side will add more redundancy on some other side which doesnt make sense and because of this wildberger is right.

>>8353631
Depending on whether you think a Plank cube can only have two states (occupied (on) or unoccupied (off)) or an infinite amount, and on the choice of base, the biggest number is actually 2^10^200 or infinity

>>8369503
a maxel is to a vexel what a matrix is to a vector

>>8369583
Why does a number need a physical representation to exist? Furthermore who caress if a number exists?

>>8369791
>Why does a number need a physical representation to exist?
An idea can't exist without a brain or a physical thing storing it. A number is just like an idea.