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Re: -2^4 vs (-2)^4
Posted:
Feb 9, 2009 10:56 PM
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On Feb 9, 2009, at 10:22 PM, Bret Taylor wrote:
> My two cents.
>
> I use several different "techniques" to try and convince my
> students that -6^2 = -36.
>
> But, this one seems to work the best:
>
> -a = -1*a
>
> So,
>
> -2 = -1*2
> -5 = -1*5
> -dog = -1*dog
> -& = -1*&
>
> therefore, -6^2 = -1*6^2
>
> And, since we do multiplication after exponentiation, -6^2 = -1*36
> = -36.
Whether or not -6^2 = -36 is completely a matter of linguistic
convention. It is certainly NOT a matter of logic. Just try to
formalize the above.
It is of course true that for this or that reason, this or that way
of coding may or may not facilitate computations. For instance, if,
in analysis, f(x) is the preferred notation, in algebra, fx and even
xf have very strong proponents.
It may or may not be worth class time to show that agreeing to read
the - as affecting 6^2 is better suited to the computations we will
be likely doing in the foreseeable future than looking at - as
automatically being the sign going with the 2. But one could
certainly argue that, inasmuch as we are dealing with signed numbers,
it is better to see the - as the sign of the integer whose size is 2
before reading anything else.
In any case, though, it is completely misleading and immensely
counterproductive to " try and convince students that -6^2 = -36".
Regards
--schremmre
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