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

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.