What I understand is that the only difference between plus and minus is direction.
I've never understood this: That
+1 + +1 is
+2, why is
-1 - -1 not
(In the first, we are moving from right to the right to the right, so we get right. In the second, we are moving from left to the left to the left, so why don't we get left?)
What's a logically/ philosophically logical/ true explanation? What are the base axioms that everything is defined upon?
Indeed, why does a negative(left) number times a positive(right) number equal negative(left)? Shouldn't it have an undefined direction with respect to left–right?