/sci/ - Science & Math

For math to be completer

>>5198198
The question is, is that the only way?

>>5198203
Math is basically a way of expressing universal values, so probably it is.

Good question.
Why do we have to separate numbers into even and odd, prime and composite, larger and smaller, integers and non-integers, rationals and irrationals, real and imaginary?
Why can't all number just be equal, man?

>>5198203
Nope. We could have a system of numbers that describe both sides.

We don't because when language was evolving humans were primative fucks who didn't recognize the need to have words for numbers that didn't actually exist.

Suppose we begin with N, the natural numbers (0,1,2,3...). If you try to solve an equation like x+2=1, there is no solution for x in N. So, you define Z like the extension of N so that equations like that have solution; that is, (0,+-1,+-2,+-3,...).

Because you can add an apple to another one or remove an apple from the other one, thus: +1 and -1

>>5198203
I will assume we are talking about whole numbers. If the problem is that not every natural number is the successor of another, then you do not have to add negative numbers to your mathematical system. You can also modify the peano axiom that "0 is no successor" by turning it into "There is a finite amount of numbers" and then you have modulo arithmetic ( http://en.wikipedia.org/wiki/Modulo_arithmetic ), which doesnt have to deal with negative numbers.
Did that solve your problem? If not, please specify it.

>>5198221
Could we devise a mathematical system that wouldn't require negative numbers and would still be capable of expressing every science wholly?

>>5198226
If we are operating on vectors in n>=2-dimensional space, you can define each vector as a combination of length and n-1 angles of rotation to a given axis, none of which have to use negative numbers. For example, complex numbers have the system of polar coordinates.
Did that solve your problem? If not, please specify it. (I repeat that because from experience, people dont do it if I dont tell them to.)

>>5198234
Thanks for answering. If I understand this correctly, signing is a matter of definition and not some inherent property of complexities that arise with abstract thought.

>>5198226 No we need negative numbers, (negative in the context of the traditional axioms) these negative numbers signify a direction. Without direction one dimensional systems would not be logically sound in any application of science. Negative numbers have far reaching implications in reality.

>>5198242
You can get signing by starting with complex numbers and then restricting the angle of rotation to the values 0 and pi. The absolute value of the complex number is then the absolute value of the real number, while the angle determines the sign.

Maybe the concept of countability will help you: You can write down two columns of number next to each other, that extend downwards into infinity, such that one contains each natural number once, and the other each whole number once. Therefore, you can define the n-th whole number to be that one that shows up next to n in the column of natural numbers, and have no need for signs.

>>5198234

on a line

(1,pi)=-1

well, that saved a lot of work, eh?

>>5198437
I did say that in >>5198271
But what work does it save?