mathematical induction

English

Noun

mathematical induction (countable and uncountable, plural mathematical inductions)

1. (mathematics) 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 $n\geq 0$, $P(n)$ implies $P(n+1)$, then $P(n)$ is true for any natural number n.
   • 2007, Mark Bridger, REAL ANALYSIS: A Constructive Approach, Hoboken, New Jersey: John Wiley & Sons, page 2:

     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

method of proof

• Chinese:

  Mandarin: 數學歸納法／数学归纳法 (shùxué guīnàfǎ)

• Polish: indukcja matematyczna f
• Tagalog: sipnaying pamuuran