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Encyclopedia article stating the principle of transfinite induction over ordinals, including its zero, successor, and limit cases, plus transfinite recursion and its relation to the axiom of choice. Readers learn how to structure proofs indexed by ordinals.
More resources on Transfinite Induction
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.
Set Theory
Learn set theory with Aleph 0! This course covers transfinite induction and more.
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.