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

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Dave L. Renfro

Posts: 4,514
Registered: 12/3/04
Re: Proving a definition of multiplication (wrong) by induction
Posted: Jan 29, 2013 10:02 AM
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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


Date Subject Author
1/28/13
Read Proving a definition of multiplication (wrong) by induction
Jonathan Crabtree
1/29/13
Read Re: Proving a definition of multiplication (wrong) by induction
GS Chandy
1/29/13
Read Re: Proving a definition of multiplication (wrong) by induction
Dave L. Renfro
1/29/13
Read Re: Proving a definition of multiplication (wrong) by induction
Jonathan Crabtree
1/29/13
Read Re: Proving a definition of multiplication (wrong) by induction
Jonathan Crabtree
1/30/13
Read Re: Proving a definition of multiplication (wrong) by induction
Dave L. Renfro
1/31/13
Read Re: Proving a definition of multiplication (wrong) by induction
GS Chandy
2/1/13
Read Re: Proving a definition of multiplication (wrong) by induction
Jonathan Crabtree
2/4/13
Read Re: Proving a definition of multiplication (wrong) by induction
Dave L. Renfro
2/4/13
Read Re: Proving a definition of multiplication (wrong) by induction
Robert Hansen
2/4/13
Read Re: Proving a definition of multiplication (wrong) by induction
Jonathan Crabtree
2/5/13
Read Re: Proving a definition of multiplication (wrong) by induction
Robert Hansen
2/5/13
Read Re: Proving a definition of multiplication (wrong) by induction
GS Chandy
2/5/13
Read Re: Proving a definition of multiplication (wrong) by induction
GS Chandy
2/5/13
Read Re: Proving a definition of multiplication (wrong) by induction
Dave L. Renfro
2/5/13
Read Re: Proving a definition of multiplication (wrong) by induction
Fernando Mancebo
2/6/13
Read Re: Proving a definition of multiplication (wrong) by induction
Jonathan Crabtree
2/6/13
Read Re: Proving a definition of multiplication (wrong) by induction
GS Chandy
2/6/13
Read Re: Proving a definition of multiplication (wrong) by induction
GS Chandy
2/8/13
Read Re: Proving a definition of multiplication (wrong) by induction
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