
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

