Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Proving a definition of multiplication (wrong) by induction
Replies: 19   Last Post: Feb 8, 2013 2:36 AM

 Messages: [ Previous | Next ]
 Dave L. Renfro Posts: 4,791 Registered: 12/3/04
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?

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

Date Subject Author
1/28/13 Jonathan Crabtree
1/29/13 GS Chandy
1/29/13 Dave L. Renfro
1/29/13 Jonathan Crabtree
1/29/13 Jonathan Crabtree
1/30/13 Dave L. Renfro
1/31/13 GS Chandy
2/1/13 Jonathan Crabtree
2/4/13 Dave L. Renfro
2/4/13 Robert Hansen
2/4/13 Jonathan Crabtree
2/5/13 Robert Hansen
2/5/13 GS Chandy
2/5/13 GS Chandy
2/5/13 Dave L. Renfro
2/5/13 Fernando Mancebo
2/6/13 Jonathan Crabtree
2/6/13 GS Chandy
2/6/13 GS Chandy
2/8/13 salesmachine