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):
> 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 proof
by induction" , it does not follow that the result is not true.
Maybe it can be proved by another method.
 By the way, this is not clearly phrased. Do you mean every
proof by induction must fail or some proof by induction must fail?
Also, I think you're using the term "proof" differently than
mathematicians use it (i.e. a logically correct argument), even
aside from the liberal use of "proof of a defintion" (by which
I assume you mean something like "a proof that something or
other fits the criterion for a definition").
Dave L. Renfro