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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: 4,560
Registered: 12/3/04
Re: Proving a definition of multiplication (wrong) by induction
Posted: Feb 4, 2013 5:51 PM
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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
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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