Meaning of mathematical induction | Babel Free

Definitions

A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n.

countable, uncountable

Examples

“Mathematical induction is often compared to the behavior of dominos. The dominos are stood up on edge close⟳ to each other in a long row. When one is knocked over, it hits the next one (analogous to n in S implies n + 1 in S), which in turn⟳ hits the next, etc. If then we hit the first (0 in S), then they will all eventually fall⟳ (S is all of #92;mathbb#123;N#125;). In Variation 1 above, we start⟳ by knocking over the kth domino, so that it and all subsequent ones eventually fall⟳.”

CEFR level