Ah, you would like a simple "Algebra" problem, yes?
Alright here we go:
Suppose that I have a set I containing all of the positive "odd" integers
I = {n | n > 0 ^ n % 2 = 1}
The first rule of addition is this:
n + (n + 1) --> (n (n + 1) - n ) V (n > (n + 1) --> n - (n + 1))
The above states to subtract the lesser integer from the greater integer depending on the position of the quantities. This essentially eliminates the commutative property of addition, and by extension, multiplication.
Due to this, "I" is a mathematical group. It has the addition binary operation available. |