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Subject: Re: any number raised to zero power should be positive  one
Date: Mon, 30 Mar 2009 02:36:01 +0000 (UTC)
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"Steven Lord" <slord@mathworks.com> wrote in message <gqp839$p7a$1@fred.mathworks.com>...
> .......
> Note that what you wrote in your subject is not technically true.  There's 
> one number that, when raised to the 0th power, does not result in 1.  That 
> number is NaN -- NaN^0 results in NaN.
> .......

  There is also another number to the zero-th power that is indeterminate in the world of calculus and that is zero to the zero-th power.  Its limiting value depends, as is characteristic of all indeterminate forms, on how fast the two quantities x and y in x^y respectively approach zero.  It can be made to approach any value between zero and one or oscillate endlessly between the two without a limit.

  Nevertheless my matlab version does return a one in this case.  However, my hand calculator correctly indicates "error".  I have a vague memory of someone on CSSM complaining about that at some time in the very distance past.  (Perhaps it was I -  I can't remember.)

Roger Stafford