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The use of the principle of mathematical induction in a proof. Induction used in mathematics is often called mathematical induction.
The truth of an infinite sequence of propositions P_i for i=1, ..., infty is established if (1) P_1 is true, and (2) P_k implies P_(k+1) for all k. This principle is ...
Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...
The fifth of Peano's axioms, which states: If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.
Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that the interval [0,n] is contained in D, one can show ...
Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that n is in D, one can show that n+1 is also in D. ...
The "mathematical paradigm" is a term that may be applied to the fundamental idea that events in the world can be described by mathematical equations, and that solutions to ...
The William Lowell Putnam Mathematics Competition is an annual mathematics contest open to North American college students administered by the Mathematical Association of ...
The Egyptian Mathematical Leather Roll (EMLR), dates to the Middle Kingdom, and was purchased in Egypt in 1858 by Henry Rhind, near the time when the Rhind papyrus was ...
Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...
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