mathematical induction

Noun

 * 1)  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 $$n \ge 0$$, $$P(n)$$ implies $$P(n + 1)$$, then $$P(n)$$ is true for any natural number n.
 * 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 $$\mathbb{N}$$). In Variation 1 above, we start by knocking over the kth domino, so that it and all subsequent ones eventually fall.
 * 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 $$\mathbb{N}$$). In Variation 1 above, we start by knocking over the kth domino, so that it and all subsequent ones eventually fall.

Translations

 * Chinese:
 * Mandarin: 數學歸納法
 * Polish: indukcja matematyczna
 * Tagalog: sipnaying pamuuran