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The Principle of Mathematical Induction ... Mathematical Induction is way of formalizing this kind of proof so that you don't have to say "and so on" or "we keep on going this way" or some such statement. ... Another form of Mathematical Induction is the so-called Strong Induction described below.
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www.math.sc.edu/~sumner/numbertheory/induction/Inductio...
www.math.sc.edu/~sumner/numbertheory/induction/Induction.html
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A type of proof that deserves special attention is mathematical induction. Some of the statements of theorems which can be proved using mathematical induction involve an integer variable. An example of such a theorem is...
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www.math.csusb.edu/notes/proofs/pfnot/node10.html
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Mathematical proof - Wikipedia, the free encyclopedia
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In mathematics, a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning,...
en.wikipedia.org/wiki/Mathematical_proof
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In Math B30 we consider mathematical induction, a concept that goes back at least to the time of Blaise Pascal (1623 - 1662) when he was developing his "Triangle". ... I'm sure that we're all more than familiar and probably tired of the standard problems on induction such as:
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mathcentral.uregina.ca/RR/database/RR.09.95/nom3.html
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If we add k + 1 to both sides of the equality in S(k), then on the left side of the sum, we obtain the left side of equality in S(k + 1). Our hope is that the right of the sum equals the right side of S(k + 1). Let us check: Adding K + 1 to both sides of S(k) we get: 1 + 2 + 3 + ...
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math.usask.ca/emr/examples/nduc_eg1.html
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Mathematical induction is a common method for proving theorems about the positive integers, or just about any situation where one case depends on previous cases. Here’s the basic idea, phrased in terms of integers:
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www2.edc.org/makingmath/mathtools/induction/induction.a...
www2.edc.org/makingmath/mathtools/induction/induction.asp
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(Proof by Mathematical Induction) Let's let P(n) be the statement "1 + 2 + ... + n = (n (n+1)/2." (The idea is that P(n) should be an assertion that for any n is verifiably either true or false.) The proof will now proceed in two steps: the initial step and the inductive step.
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zimmer.csufresno.edu/~larryc/proofs/proofs.mathinductio...
zimmer.csufresno.edu/~larryc/proofs/proofs.mathinduction.html
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Interactive Induction ... :: PDF format :: Naoki Sato's solutions PDF :: Naoki Sato's info :: Spanish Version :: Contact :: A Catalog of Mathematics Resources :: Art of Problem Solving :: Interactive Mathematics Miscellany and Puzzles :: Mathematical Problems - Problem Solving :: Mathematics Archives ::
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www.math.cl/induction.html
www.math.cl/induction.html
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