Boulet
Posts:
84
Registered:
12/3/04
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Re: neg * neg = pos; why?
Posted:
Jul 23, 1997 3:23 PM
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Here is my answer to your question below.
Looking for patterns is nice, it can help us predict the next value, but
does it explain its reason for being? That is what missing in such
reasoning. People want to know WHY such a pattern occurs. Is it magic or
is there a reason? In the case of negative numbers, an understanding of
negative numbers as well as the operations with them cannot be reduced to
mere pattern recognition. The historical struggle for their acceptance and
their conceptualization as directed numbers is well worth looking at.
Gen.
>When students ask me these questions, I usually respond like this:
>
>3 * -5 = -15, right?
>2 * -5 = -10.
>1 * -5 = -5.
>0 * -5 = 0.
>
>So what's the pattern? We keep adding 5 to the right side each time.
>
>Similarly, I use this kind of pattern to explain why 0! whould equal
>1, and why 5^0 should = 1 and 5^(-1) should be 1/5.
>
>What do you think of this kind of reasoning?
>
>--Joshua
>
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