Set Fundamentals

Discrete Math · Axiom Academy

The foundation of modern mathematics: understanding sets, membership, subsets, and the notation that brings them to life. The fundamental relationship is membership : we write x ∈ A to mean "x is an element of A" and x ∉ A to mean "x is not an element of A." 2. Roster vs. Set-Builder Notation There are two main ways to describe sets: Set-builder notation uses the form x | P(x) or x : P(x) , read as "the set of all x such that P(x) is true." Mathematics uses standard symbols for frequently-used sets of numbers: 4. Subsets and Set Relationships If A ⊆ B but A ≠ B, we say A is a proper subset of B, written A ⊂ B.

This is the written version of the interactive lesson above. See the full Discrete Math course.