the definitions are identical to a number line
+ is a move to the right
- is a move to the left
The point is, in "the universe" most of "infinity" are actually finite circles that you can travel along "infinitely" - because you eventually arrive back where you started.
and -1/12 just means 1/12 to the left before you get back where you started moving right.
sum continues to work in the same in your circle (Commutativity, Associativity, Identity element and a + 1 is the next successor of A)