Set Theory Vs. Abstract Algebra
Here's the dirt on how these objects relate to one another:
Like real analysis, many of the "algebraic" constructions are essentially just set-theoretic constructions; the biggest example being the operation of "modding out" over an equivalence relation. A decent grasp of set theory is essential to deeply understand, for example, the transition from the standard integers to the integers mod N.
In turn, set theory benefits from algebra because you can treat sets as an algebraic structure, with union and intersection being analogous to addition and multiplication.
In turn, set theory benefits from algebra because you can treat sets as an algebraic structure, with union and intersection being analogous to addition and multiplication.