
Re: Proving a definition of multiplication (wrong) by induction
Posted:
Jan 29, 2013 10:02 AM


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 proof by 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 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

