Single Idea 17936

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction]

Full Idea

Transfinite inductions are inductive proofs that include an extra step to show that if the statement holds for all cases less than some limit ordinal, the statement also holds for the limit ordinal.

Gist of Idea

Transfinite induction moves from all cases, up to the limit ordinal

Source

Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1 n11)

Book Reference

Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.83