I'm working on addition and multiplication axioms of integers for discrete math. I'm trying to prove
(k - m) + (m - n) = k - n. The first step I took was this (without citing any of the axioms):
= k + (-m) + m + (n)
Is this incorrect?
On a related note, the solution in the textbook on the other hand starts off like this:
= (k + (-1)m) + (m + (-1)n) = k + [(-1)m + m + (-1)n)
(-1)m + m is zero. What I don't understand is how do they go from step 1 to step 2?
The axioms I'm given are as follows: