set theory: Quick Facts

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Nov. 8, 2026

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Which infinity is bigger? Under alternative mathematical rules, a 2D map emerges • Nov. 5, 2026, 9:40 AM ET (Phys.org)

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$A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”$

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Topics

generalized continuum hypothesis union axiomatic set theory measure theory complement principle of abstraction intersection axiom of infinity axiom of separation axiom schema of replacement analysis probability theory cryptology computer science combinatorics algebra statistics geometry automata theory information theory

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Key People

Georg Cantor

Georg Cantor

German mathematician

Paul Erdős

Paul Erdős

Hungarian mathematician

John von Neumann

John von Neumann

American mathematician

Saul Kripke

Saul Kripke

American logician and philosopher

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Stanislaw Ulam

American scientist

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Paul Joseph Cohen

American mathematician

Equations written on blackboard

Numbers and Mathematics