# mathematical induction

**mathematical induction** Method of proving that a mathematical statement is true for any positive integer *n* by proving: (1) that it is true for a base value, for example 1; and (2) that if it is true for a value *k* then it is also true for *k* + 1. If (1) and (2) hold, then it follows in a finite number of steps that the statement is true for any positive integer *n*.

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Induction (logic) , In mathematics, induction is a technique for proving certain types of mathematical statements. The induction principle can be illustrated by arrangin… Encyclopedia.com. , true / troō/ • adj. (tru·er , tru·est ) 1. in accordance with fact or reality: a true story of course it's true that is not true of the people I am t… Proof (mathematics) , Proof
A proof is a logical argument demonstrating that a specific statement, proposition, or mathematical formula is true. It consists of a set of as… Number , Number
Numbers are central to science. They underlie what Galileo Galilei and Isaac Newton called the primary properties of things, the properties th… Theorem , Theorem
A theorem (the term is derived from the Greek theoreo, which means I look at ), denotes either a proposition yet to be proven or a propositio… Consistency , Mathematics contains a number of different systems, but each mathematical system, no matter how different it may be from another, has consistency as…

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