principle of mathematical induction
 principle of mathematical induction

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 of all positive integers. Cf.
induction (
def. 5).
* * *
Universalium.
2010.
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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
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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 — • 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
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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