# mathematical induction

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mathematical induction
The principle stating that for all properties, given that a property holds of the number 1, and given that when it holds of one number it holds of its successor, then it holds of all positive numbers.

Philosophy dictionary. . 2011.

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• 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

• mathematical induction — induction (def. 5). [1830 40] * * * …   Universalium

• mathematical induction — noun Date: 1838 induction 2b …   New Collegiate Dictionary

• mathematical induction — noun : induction 2b(2) …   Useful english dictionary

• principle of mathematical induction — Math. a law in set theory which states that if a set is a subset of the set of all positive integers and contains 1, and if for each number in the given set the succeeding natural number is in the set, then the given set is identical to the set… …   Universalium

• principle of mathematical induction — Math. a law in set theory which states that if a set is a subset of the set of all positive integers and contains 1, and if for each number in the given set the succeeding natural number is in the set, then the given set is identical to the set… …   Useful english dictionary

• Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …   Wikipedia

• 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

• Mathematical proof — In mathematics, a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true.[1][2] Proofs are obtained from deductive reasoning, rather than from inductive or empirical… …   Wikipedia

• Induction — Most common meanings * Inductive reasoning, used in science and the scientific method * Mathematical induction, a method of proof in the field of mathematics * Electromagnetic induction in physics and engineering Other articles * Induction (play) …   Wikipedia