Epsilon-induction is a method of proof in the field of mathematical logic and set theory that extends the principle of mathematical induction. It is typically used in the context of transfinite induction and is useful in dealing with well-ordered sets. In standard mathematical induction, one proves a statement for all natural numbers by demonstrating two things: 1. The base case: the statement holds for the smallest natural number (typically 0 or 1).
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The principle of epsilon induction says that every progressive class is universal: ifthen holds for every set . Over the other axioms of ZF, it is equivalent to the Axiom of foundation.