The principle of mathematical induction

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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

• 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 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

• 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 — inductionless, adj. /in duk sheuhn/, n. 1. the act of inducing, bringing about, or causing: induction of the hypnotic state. 2. the act of inducting; introduction; initiation. 3. formal installation in an office, benefice, or the like. 4. Logic.… …   Universalium

• 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

• 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

• Mathematical jargon — The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in… …   Wikipedia

• The Seven Liberal Arts —     The Seven Liberal Arts     † Catholic Encyclopedia ► The Seven Liberal Arts     The expression artes liberales, chiefly used during the Middle Ages, does not mean arts as we understand the word at this present day, but those branches of… …   Catholic encyclopedia

• History of the Church–Turing thesis — This article is an extension of the history of the Church–Turing thesis. The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …   Wikipedia