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Induction
Induction or inductive may refer to: Biology and medicine * Labor induction (of birth) * Induction chemotherapy, in medicine * Enzyme induction and inhibition * General anaesthesia Chemistry * Induction period, slow stage of a reaction * Inductive cleavage, in organic chemistry * Inductive effect, change in electron density * Asymmetric induction, preferring one stereoisomer over another Computing * Grammar induction * Inductive bias * Inductive probability * Inductive programming * Rule induction * Word-sense induction Mathematics * Backward induction in game theory and economics * Induced representation, in representation theory * Mathematical induction, a method of proof ** Strong induction ** Structural induction ** Transfinite induction *** Epsilon-induction * Parabolic induction Philosophy * Inductive reasoning, in logic Physics * Electromagnetic induction * Electrostatic induction * Forced induction, or turbocharging, of an engine Other uses * Inducti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematical Induction
Mathematical induction is a method for mathematical proof, proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for n = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case n = k, ''then'' it must also hold for the next case n = k + 1. These two steps establish that the statement holds for every natural number n. The base case does not necessarily begin with n = 0, but often with n = 1, and possibly with any fixed natural number n = N, establishing the trut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
