Set Theory
Dr. Trefor Bazett
Learn set theory & explore cardinality with Dr. Trefor Bazett's course. Master the fundamentals through this accessible YouTube playlist!
More resources on Cardinality
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab: Cardinality
The nLab wiki entry on cardinality, defining cardinal numbers as isomorphism classes of sets and discussing them from category-theoretic and constructive perspectives. Useful for readers who already know basic set theory and want the structural view of size.
Hilbert's Infinite Hotel Paradox
A short animated TED-Ed lesson by Jeff Dekofsky that walks through Hilbert's paradox of the Grand Hotel. Viewers see why a full infinite hotel can still accommodate new guests, building intuition for countable infinity and one-to-one correspondence.
How To Count Past Infinity
A Vsauce video by Michael Stevens explaining ordinal and cardinal numbers, from counting with omega to the distinction between countable and uncountable sets. Viewers come away understanding why some infinities are larger than others and how transfinite counting works.
Stanford Encyclopedia of Philosophy - Set Theory
Joan Bagaria's peer-reviewed Stanford Encyclopedia of Philosophy entry surveying modern set theory: the ZFC axioms, ordinals and cardinals, the continuum hypothesis, forcing and independence results, large cardinals, and determinacy. Readers gain a map of the field's central questions and results.
Introduction to Mathematical Thinking
Stanford course by Keith Devlin on how mathematicians reason, starting with the logic of language (and, or, not, implication, quantifiers) and moving to the structure of proofs, including contradiction and induction. Learners become able to read, construct and critique simple mathematical proofs.