I'm not a mathematician but I'm studying Nothing, so 0 is relevant, and I'm wondering about the fact that numbers seem to be mutually canceling polarities extending from 0, that is
0 = n - n or
0 = (+n) + (-n) and:
...-2, -1, 0, 1, 2...
...-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2...
So at the very least if you equally extend two collection of numbers from 0 in both directions and sum them it will always equal 0, but I'm not sure what would happen if you have two sets with all the numbers in both directions, as well as an infinite fractional resolution between whole numbers, because then both the sets would be infinite, or negative and positive infinities
0 = (+Infinite) + (-Infinite), that is if that makes sense (not sure how you would define e.x. infinite positive whole numbers).
Also I seem to remember that there is something called "complex numbers" which aren't present on the number line.
- Summing a finite set of polarizing whole numbers extending from 0 with a finite resolution between whole numbers will always equal 0.
- Is this also true if we include more numbers then the ones on the number line (complex numbers, etc)?
- Is this also true for an infinite number of whole numbers with an infinite fractional resolution?
"The sum of all numbers equals 0"True?
- Is there any formal way to define
The calculation I'm interested in also has these arbitrary restrictions:
- "all numbers" means all numbers with only one instance of each number within the formula
- the order of the numbers in the calculation is 0+(+1)+(-1)+(+2)+(-2)... etc.