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