Algebra is the study of generalizations that can be made about arithmetic. For example: In arithmetic, it’s a true proposition that 1 + 2 = 2 + 1. It’s also a true proposition that 2 + 3 = 3 + 2. However, in algebra those two propositions, and infinitely more like them, can be generalized into the proposition that for all numbers x and y, x + y = y + x.