There are no numbers other than the naturals Prove me wrong

>>8664245
Well we have to start with some rules of discourse, I assume you allow the rules of set theory and classical logic. Now, start with the assumption that anything that can be constructed with these rules and the natural numbers are also numbers.

We construct the rational numbers as so:

[math]S = \left{(x,y) \in \mathbb{N} \times \mathbb{N} | y \neq 0 \right} [/math]

Then the set of rational numbers are the equivalence classes of the set [math]S[/math], under the relation

[math](a,b) \simeq (c,d) \iff ad = bc [/math]

One such equivalence class is:

[math]\left{(1,2), (2,4), (3,6), \dots \right} [/math] corresponding to the rational number which we denote by [math]\frac{1}{2}[/math]

>>8664257
Just to clean things up, I mean
[math]S = \{(x,y) \in \mathbb{N} \times \mathbb{N} | y \neq 0 \} [/math]
and

[math]\{(1,2), (2,4), (3,6), \dots \} [/math]

>>8664245
Unironically I agree. In reality there are only natural numbers, one half of an apple is an half apple, not one half of one apple.

>>8664282
1 is the only number? Sounds like a pretty retarded system.

there are no numbers in nature

>>8664282
That's absurd. Even if you were to prove that everything in the universe is discrete you still would want the reals and the complex numbers to calculate things

>>8664313
>the computable reals and computable complex numbers
fixed

>>8664282
But then I could say that there are no other numbers than 1. No two things can be exactly the same, so you can never have 2 of the same thing.

There are no 2 apples, there is one apple, and one slightly different apple.

>>8664316
what if computability in this regard is merely a temporal constraint and not one that prevents algebraic structure to define the transcendental?

>>8664319
Well yeah. Its categorization of things, those categories can then be broken into countable parts.

Math is an illusion, a useful one, but an illusion none the less

>>8664365
A computable real is one that is possible to algorithmically approximate (with rationals) to arbitrary degree. There are numbers where this is not possible.

Some transcendental numbers like π or e are computable, but most will not be, since there is a countable number of programs.

>>8664245
OP is a retard: the thread

Stat with Counting - whole numbers
> But zog, who needs more than 1,2, many

Add zero
> How can "nothing" be a thing

Add fractions
> What is half a person? Nonsense

> Add negatives
How can something be less than nothing. I am calling you out for sorcery.

Note that negative numbers are just positive numbers in the opposite direction. So real numbers have two directions only.

Add irrational numbers
> How can an irrational thing be a number
> keep this secret

Add numbers in all directions. + = East, - = West, i = North, -i = South.
> I am a practical man. Why would I need these so-called imaginary numbers?

>>8664245
Pi

>>8664282
>one half of an apple is ... not one half of one apple.

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>>8664245
The area of this circle is 1 square unit
What's it's radius?

>>8664245
if zero isn't a natural number, then you are a pleb

>>8664245
Let me explain you one thing. Traditional mathematics have for them something that your wilderberger paradigm don't have.
Maybe the real numbers don't exist. I don't care. Because even if they don't they provided the physical basis that was needed to build your house, and the roads and bridges you're driving on, and the computer you're browsing on. So even if they don't exist, they are useful.

Take your paradigm, and show me it is more useful than the classical one, that it is more powerful, that it allows a better resolution of problems. Then I'll take you seriously.
For the moment, allow me to laught at you.

The so-called "natural" numbers
are as artificial as an alarm clock.

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>>8664282

>>8664690
i hate when they make math all about the numbers. numbers don't exist. order and relations do.

>>8664245
Actually no one can disprove you, by Lowenheim-Skolem. Everything *can* be mapped inside of the natural numbers, even though its structure will not have much to do with the natural structure on N.

>>8664639
YOU FOOL
There is no circle in nature
There is no radius for a circle in nature
There are no square units in nature
There is no area in real world, only 3-dimensional objects
If you want to know how big a plot of land is, you merely need to count the grains of sand or something similar inside it. All of which can be counted with natural numbers.
Irrational numbers exist only inside an irrational mind.

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>>8664245
Plebs there are only two numbers.
0 and 1.
Yes or No.
Every number is only a sequence of 0s and 1s.
Every other field or group is only a set of functions on those sequences.

>>8664668
>laught
Is this a pasta? If not, it should be

>>8664717
typical "objects are just there to hang arrows on" autist

>>8664245
Why would I want to prove you wrong?
I think you spoke rationally, sanely, intelligently.
I think people who believe in and use irrational numbers are irrational.

Besides, no one can prove anything: true or false. We have only our best, common-sense judgment of what model works best and safest or we are mindless believers in certainty in an uncertain Reality.

>>8664319
>No two things can be exactly the same
but indistinguishable particles bro

>>8664245
Numbers Are a idea we made that is designed to formulate our environment into a ledger. It's a picture we've drawn and recognize

>>8664668
Ive always wondered about the possibility that there may be a better way to calculate the universe in a more applicable way than mathematics.