My math fu is not good, but am I understanding this correctly: In Z/Z, every integers "maps" to 0, so 2+2=5 is equivalent to 0+0=0, so 2+2=5 is true in that system...?
yes, this is what i understood too, the definition of the set states that every element is equivalent (not equal though) to the number itself modulo 1. so every element from Z is actually equivalent to 0. and, 2+2 = 4 = 0+0 = 5 = 0
given the definition of the space/set; it's true but why would we want to work on such a space where 2 + 2 does not even have a meaning? also, i wonder if there are any benefits of working inside a space/set where every element is equivalent to modulo 1 of itself.