transfinite induction

Suppose Φ(α) is a property defined for every ordinalMathworldPlanetmathPlanetmath α, the principle of transfinite inductionMathworldPlanetmath states that in the case where for every α, if the fact that Φ(β) is true for every β<α implies that Φ(α) is true, then Φ(α) is true for every ordinal α. Formally :


The principle of transfinite induction is very similar to the principle of finite induction, except that it is stated in terms of the whole class of the ordinals.

Title transfinite induction
Canonical name TransfiniteInduction
Date of creation 2013-03-22 12:29:03
Last modified on 2013-03-22 12:29:03
Owner jihemme (316)
Last modified by jihemme (316)
Numerical id 10
Author jihemme (316)
Entry type TheoremMathworldPlanetmath
Classification msc 03B10
Synonym principle of transfinite induction
Related topic PrincipleOfFiniteInduction
Related topic InductionMathworldPlanetmath
Related topic TransfiniteRecursion