transfinite induction


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transfinite induction

[tranz′fī‚nīt in′dək·shən]
(mathematics)
A reasoning process by which if a theorem holds true for the first element of a well-ordered set N and is true for an element n whenever it holds for all predecessors of n, then the theorem is true for all members of N.

transfinite induction

(mathematics)
Induction over some (typically large) ordinal.
References in periodicals archive ?
The fact that Gentzen's proof can be interpreted in the natural numbers shows that the arithmetical statement which corresponds via coding to the theorem validating transfinite induction as far as [[Epsilon].
Thus, to return to the case in hand, transfinite induction as far as [[Epsilon].