A textbook in progress for a first course in Real Analysis.

A singleton set is a set with one element. There is "essentially just one" singleton set. This a very different situation than that for the empty set, where we know there's precisely one empty set. Why? How?

Every function between sets gives rise to a function between their power sets, in the opposite direction. Power sets are Boolean algebras, and this function between power sets preserves the Boolean algebra structure: it is a morphism of Boolean algebras. This we explain and prove.

From topology to measure theory, being comfortable around unions and intersections is very important. Here we give examples and go over the definitions.

Dot products are ubiquitous in math and physics. In this YouTube video, we use dot products to visualize... dot products.