transfinite induction

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.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

transfinite induction

(mathematics)

Induction over some (typically large) ordinal.

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