About: Mathematical induction

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Mathematical induction is a method of proof by which a statement about a variable can be demonstrated to be true for all integer values of that variable greater than or equal to a specified integer (usually 0 or 1). An example of such a statement is: * The number of possible pairings of n distinct objects is (for any positive integer n). A proof by induction proceeds as follows: That the conclusion in step 3 above follows from steps 1 and 2 is the principle of mathematical induction. 1. * * The conclusion is then 1. * for .

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rdfs:label	Mathematical induction
rdfs:comment	Mathematical induction is a method of proof by which a statement about a variable can be demonstrated to be true for all integer values of that variable greater than or equal to a specified integer (usually 0 or 1). An example of such a statement is: * The number of possible pairings of n distinct objects is (for any positive integer n). A proof by induction proceeds as follows: That the conclusion in step 3 above follows from steps 1 and 2 is the principle of mathematical induction. 1. * * The conclusion is then 1. * for .
sameAs	dbr:Mathematical_induction
dcterms:subject	Proofs Articles containing proofs Proof Proof theory Inductive reasoning Mathematical logic Logic
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abstract	Mathematical induction is a method of proof by which a statement about a variable can be demonstrated to be true for all integer values of that variable greater than or equal to a specified integer (usually 0 or 1). An example of such a statement is: * The number of possible pairings of n distinct objects is (for any positive integer n). A proof by induction proceeds as follows: 1. * The statement is proved for the first possible value of n (usually 0 or 1, but other "starting values" are possible). 2. * The statement is assumed to be true for some fixed, but unspecified, value n and this assumption is used to prove that the statement is true for (the latter statement is simply the original statement with n replaced by ). 3. * The statement is then concluded to be true for all relevant values of n (all nonnegative values or all positive values, depending). That the conclusion in step 3 above follows from steps 1 and 2 is the principle of mathematical induction. More formally, given a proposition about the integer-valued variable n that is to be proved for , the following must be proved. 1. * * The conclusion is then 1. * for .

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