Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers.
Read more about Transfinite Induction: Transfinite Induction, Transfinite Recursion, Relationship To The Axiom of Choice
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“They relieve and recommend each other, and the sanity of society is a balance of a thousand insanities. She punishes abstractionists, and will only forgive an induction which is rare and casual.”
—Ralph Waldo Emerson (1803–1882)