# Set Theory
Confidence: high
Last verified: 2026-05-22
Generation: human_only


## TL;DR

Set theory (Georg Cantor, 1874) is the language of mathematics — almost all mathematical objects can be defined as sets. A set is a collection of distinct objects. Operations: union (∪), intersection (∩), difference (−), complement. Used in: databases (SQL JOINs), type theory, probability.

## Core Explanation

Set A = {1, 2, 3}. Subset: A ⊆ B means every element of A is in B. Power set P(A): all subsets of A — 2^n subsets for n elements. Russell's Paradox (1901): the set of all sets that don't contain themselves — exposed flaws in naive set theory. ZFC (Zermelo-Fraenkel with Choice) is the modern axiomatic foundation.

## Further Reading

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