How do you prove that negative numbers exist?

how do you prove that positive numbers exist?

How do you prove that anything exists at all?

How do you prove that a proof is true?

>>8727808
Overdraft my credit card, boom negative numbers

>>8727808
Look at my bank balance.

>>8727822
>How do you prove that anything exists at all?

I think, therefor I am.

>How do you prove that a proof is true?
If logic is real, then I can use logic. If logic isn't real, then I don't need proof because proof is a logical construct.

Checkmate

>>8727824
>>8727825
Hey, you took my joke!

>>8727808
Because what can be negative has to be positive.
What has, can be.

>>8727808
Assume positive numbers exist
Define a set as the Cartesian product of the positive numbers.
Define some operators on your new set
(a,b)+(c,d) = (a+c, b+d)
(a,b)*(c,d) = (ac+bd, bc+ad)
Define an equivalence relation
(a,b) ~ (c,d) iff a+d = b+c
Create an equivalence class from your new set and equivalence relation.
The negative numbers are the subset of your equivalence class
{(a,b) in EC : b<a }

>>8727828
Low hanging fruit, I guess.

>>8727808
any numbers doesnt exist without something else

like you can have 2 apples

but you can't have just 2

it' d be like 2 nothings

>>8727808
The natural numbers don't form a group with addition. The integers do form a group with addition because each positive number has an inverse (the negative number of equal magnitude).

So no, negative numbers don't exist unless you want to start working in a ring which you ideally do because most of our results in number theory are technically specific cases of ring theory.

>>8727824
Your credit balance is negative, the bank owes you money.

File: cat-unimpressed.jpg (53KB, 403x403px) Image search: [Google]

53KB, 403x403px

https://en.wikipedia.org/wiki/Platonic_realism

>>8727824
>>8727825
Just because you owe doesn't mean you have a negative amount of money.

Your debt is a natural number that you subtracted from your current amount which you can colloquially recognize as a negative amount of money.

How manny niggers do you need to start a riot?

-1

Here's your proof

>>8727808
Define exist

>>8727808
You can let your bank account be represented by them, slowly your belongings will dissapear.
That is clear proof of the existence of negative numbers.