```Date: Jan 29, 2013 10:02 AM
Author: Dave L. Renfro
Subject: Re: Proving a definition of multiplication (wrong) by induction

Jonathan Crabtree wrote (in part):http://mathforum.org/kb/message.jspa?messageID=8183575> Multiplication* an arithmetical operation, defined initially in> terms of repeated addition, usually written a × b, a.b, or ab,> by which the product of two quantities is calculated: to multiply> a by positive integral b is to add a to itself b times.> > i.e. ab = a added to itself b times> > This definition fails proof by induction. > > So what other proofs can be used to prove ab does not equal> a added to itself b times?I don't follow your argument. Assuming that something "fails proofby induction" [1], it does not follow that the result is not true.Maybe it can be proved by another method. [1] By the way, this is not clearly phrased. Do you mean everyproof by induction must fail or some proof by induction must fail?Also, I think you're using the term "proof" differently thanmathematicians use it (i.e. a logically correct argument), evenaside from the liberal use of "proof of a defintion" (by whichI assume you mean something like "a proof that something orother fits the criterion for a definition").Dave L. Renfro
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