An explanation of what the Axiom of Choice really says and a discussion of its equivalents and implications.

This course deals with understanding what it means for a set to have infinite size and for two sets to have equal size (or "cardinality"). We prove Cantor's Theorem that the power set $$\mathcal{P}(A)$$ has cardinality strictly larger than $$A$$, examine the comparability of sizes by studying ordinals and cardinals (with an appearance by the Axiom of Choice), the arithmetic of cardinals, and a brief discussion of the Continuum Hypothesis.

This course prepares students to take the AP Calculus BC exam in the spring.

Set Theory serves as one of the primary foundations of mathematics, with nearly every advanced mathematics discipline requiring at least an adequate knowledge of the subject as a prerequisite. Set Theory serves to provide explanation to some of the most widely assumed things in mathematics: numbers, functions, relations, etc.