Dictionary

mathematical induction en · NOUN

Meanings

1. (countable, uncountable) 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.
   • 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. 2007, Mark Bridger, REAL ANALYSIS: A Constructive Approach, Hoboken, New Jersey: John Wiley & Sons, page 2:

Forms

Translations (3)

cmn 數學歸納法 /数学归纳法 (method of proof) · tl sipnaying pamuuran (method of proof) · pl indukcja matematyczna (method of proof)