math / Foundations / free
Set Theory
Build a language for collections, membership, and structure.
Follow the mechanism1 / 3
Membership defines a collection. A universe gives the possible elements, and a rule decides whether each one belongs to a set.
finite universeU = {1 … 12} · A ∪ B
Focus the idea
highlighted resultcomplement member
A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12}
|A|6
|B|4
result size8
universe |U|12
Union means OR: an element is highlighted when it belongs to A, B, or both. Here 8 of 12 elements qualify.
A set is defined by membership, not by order. Once the universe is named, union, intersection, and complement turn everyday “or,” “and,” and “not” into precise operations.