* * *
Universalium. 2010.
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 — 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 — 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
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
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
Mathematical descriptions of physical laws — For worded descriptions and criteria of physical laws, see Physical law. For the nomenclature used see Physical quantity and Defining equation (physics). Physical laws are often summarized by a single equation, or at least a small set of… … Wikipedia
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
