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prove by induction

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  • Induction — • Induction is the conscious mental process by which we pass from the perception of particular phenomena (things and events) to the knowledge of general truths Catholic Encyclopedia. Kevin Knight. 2006. Induction     Induction …   Catholic encyclopedia

  • induction — [in duk′shən] n. [OFr < L inductio] 1. an inducting or being inducted; installation, initiation, etc. 2. Archaic an introduction; preface or prelude 3. an inducing, or bringing about 4. a bringing forward of separate facts or instances, esp.… …   English World dictionary

  • induction, problem of — Problem of justifying the inductive inference from the observed to the unobserved. It was given its classic formulation by David Hume, who noted that such inferences typically rely on the assumption that the future will resemble the past, or on… …   Universalium

  • induction — n. 1 the act or an instance of inducting or inducing. 2 Med. the process of bringing on (esp. labour) by artificial means. 3 Logic a the inference of a general law from particular instances (cf. DEDUCTION). b Math. a means of proving a theorem by …   Useful english dictionary

  • induction — noun 1》 the action or process of inducting someone to a post, organization, etc. 2》 the action or process of inducing something. 3》 Logic the inference of a general law from particular instances. Often contrasted with deduction.     ↘the… …   English new terms dictionary

  • Mathematical induction — can be informally illustrated by reference to the sequential effect of falling dominoes. Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers (positive… …   Wikipedia

  • Structural induction — is a proof method that is used in mathematical logic (e.g., the proof of Łoś theorem), computer science, graph theory, and some other mathematical fields. It is a generalization of mathematical induction. Structural recursion is a recursion… …   Wikipedia

  • Transfinite induction — is an extension of mathematical induction to well ordered sets, for instance to sets of ordinals or cardinals. Transfinite induction Let P(α) be a property defined for all ordinals α. Suppose that whenever P(β) is true for all β < α, then P(α) is …   Wikipedia

  • Faraday's law of induction — For the relationship between a time varying magnetic field and an induced electric field, see Maxwell s equations. Electromagnetism …   Wikipedia

  • Ovulation induction — Intervention MeSH D010062 Ovulation induction is the stimulation of ovulation by medication. It is usually used in the sense of stimulation of the development of ovarian follicles …   Wikipedia

  • Epsilon-induction — In mathematics, in induction ( epsilon induction ) is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P [ x ] . If the truth of the property for x follows from its truth for all… …   Wikipedia

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