Ki Song
Posts:
221
Registered:
9/19/09
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Re: 0^0=1
Posted:
May 7, 2012 11:06 AM
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On Monday, May 7, 2012 4:51:38 AM UTC-4, Ross wrote:
>
> I'm not a mathematician, and I can't read all 380 posts in this
> thread.
>
> But, my understanding of the reason that x^0 = 1 is a consequence of
> negative exponents. E.g.
Not quite, it's the other way around. The definition that
x^-n = 1/x^n
comes from
1) x^0 = 1.
2) x^(n+m) = x^n x^m
>
> if 2^-2 equals 1/2^2 and x^a * x^b = x^(a+b), then 2^2 * 2^-2 = 2^(2 +
> -2) = 2^0.
>
> We can then expand the example to get 2^0 = 2^2 * 1/(2^2) = 1.
>
> However, if x = 0, then the derivation of a^0 = 1 no longer works:
>
> 0^2 * 0^-2 = 0*0 / (0*0) = 0/0 which is undefined.
0 to any negative exponent is not defined.
>
> Hence x^0 = 1 is based on a derivation that doesn't work for x=0, and
> hence to quote the consequence of that derivation to argue the value
> of 0^0 is plain wrong.
>
> I presume that I'm "missing something" and someone will be along to
> spank me soon.
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