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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: 4,791 Registered: 12/3/04
Re: Proving a definition of multiplication (wrong) by induction
Posted: Feb 4, 2013 5:51 PM

Jonathan Crabtree wrote:

http://mathforum.org/kb/message.jspa?messageID=8235462

> In the following;
>
> "ab = a added to itself b times" or
> "ab = a added to a b times"
>
> ...the ambiguity about what 'times' refers to is really the
> essence of any confusion with definitions involving multiplication.
>
> So to clarify, are you stating that in formal definitions,
> the word 'times' refers to the count of addends, or binary additions?

In a formal treatment one would clear up any possible ambiguity
that arises in the use of a term such as this. To me, it's a
simple matter of writing

a + a + a + ... + a

and then saying exactly how many a's are intended, or equivalently,
saying exactly how many +'s are intended. If the phrase "b times"
could be ambiguous for the intended audience, then one shouldn't
use it without additional clarification. I consider this
analogous to giving driving directions to someone by saying
something like "up there a ways you want to turn left".
How far? Are there any roads to the left before getting to
the road I'm supposed to turn left on?

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