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Re: 0^0=1
Posted:
Apr 21, 2012 12:25 AM
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"DonH" <donlhumphries@bigpond.com> wrote in message
news:zKpkr.6017$%E2.342@viwinnwfe01.internal.bigpond.com...
> "Richard Tobin" <richard@cogsci.ed.ac.uk> wrote in message
> news:jmsvh1$nml$1@matchbox.inf.ed.ac.uk...
>> In article
>> <fc51d462-6ab6-4087-97c1-63bda017042c@fv28g2000vbb.googlegroups.com>,
>> Tonico <Tonicopm@yahoo.com> wrote:
>>
>>>Or, since we're dealing with real or complex numbers, consider lim x^x
>>>= lim e^{x log(x)} , when x --> 0 ...this is a good reason to define
>>>0^0 = 1 .
>>
>> But equally one could consider the limit of 0^x.
>>
>> For integers the set mapping argument seems compelling, but when
>> dealing with the reals it seems better to leave it undefined or define
>> it explicitly if needed.
>>
>> -- Richard
>
> # Yes, 0^0 may be an arbitrary device to accommodate a computer, as
> Barron's Maths Study Dictionary excludes zero(^0) (pg.62) when defining
> the "zero exponent".
> Which still leaves, eg. 5^0 = 1.
> If I have five apples and multiply them by themselves zero times, do I
> end up with one apple?
> Also, does 5^0 = 5 * 1/5?
> Has x^0 = 1 ever been proved? Or, is it merely a convenient dogma?
x^a * x^b = x^(a+b)
x^a * x^0 = x^(a+0) = x^a
x^0 = 1
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