Discussion:  Roundtable 
Topic:  exponents 
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Subject:  RE: exponents 
Author:  Alan Cooper 
Date:  Oct 18 2004 
> I'm not trying to be argumentative or picky . . .
> . . .from observing empirically 10^5/10^2 = =10^(52) = 10^3
> and so on] it *follows* that 10^3/10^5 = 10^(2).
I don't think so.
In fact, with the repeated multiplication definition, 10^(2) does not even
exist! It only makes sense if we *define* it somehow (and of course as 1/(10^2)
is probably the only useful choice).
My concern is that, by saying "it *follows* that", we may cause some students to
lose faith in their own (correct) understunding of logical implication.
I think we can agree that *I* am the one being "picky", and so I will try to
avoid posting more on this, but will reply privately if you want to chat
further.
cheers,
Alan
 
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