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View Full Version : simple math question. plz help.

Bailey
Dec5-03, 02:43 AM
i feel kinda stupid asking this question, but what is zero to the power of zero equal to? Is it equal to zero, or one, or infinity?
or the answer will varies depending on the function since it is an indermindate power?

When i use my sci. calculator, it say error.
but, when i use a math program it say 1. And its b/c of this that i'm confuse.
wubie
Dec5-03, 02:49 AM
http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
Bailey
Dec5-03, 03:03 AM
so....i suppose mathematician favor(or assume) the answer to be 1?
btw, thanx for the link wubie.
wubie
Dec5-03, 03:17 AM
mmmm.... I'm not so sure myself. To quote part of the article:


This means that depending on the context where 0^0 occurs, you might wish to substitute it with 1, indeterminate or undefined/nonexistent.


But is seems that there are many arguments which support 00 to be equal to one.

I am sure there are some here who can provide a more informative answer than I. I just posted the link to provide an immediate answer.

Hope that it helped.

Cheers.
jcsd
Dec5-03, 04:06 AM
This is not the first time it's come up, but this illustrates some of the problems with defining 0^0 as 1:

x^{n-1} = \frac{x^n}{x}

x^1 = x

0^0 = \frac{0}{0}

\frac{0}{0} is indetrimnate, so to define 0^0 as 1 requires the (seemingly) arbitary breaking of some of the rules of algebra.

But it also came up in the other thread that sometimes there are good reasons for defining 0^0 as [itex]1[/tex], but you'll have to ask Hurkyl about that.
NateTG
Dec5-03, 03:50 PM
What 0^0 is equal to usually depends on context. I expect that in environments where it is defined, it will usually be 1.
Hurkyl
Dec5-03, 04:23 PM
Basically, the times when one says 0^0=1 are the times when the operation involved really isn't about exponentiation, but about doing something repeatedly.
NateTG
Dec5-03, 04:58 PM
Originally posted by Hurkyl
Basically, the times when one says 0^0=1 are the times when the operation involved really isn't about exponentiation, but about doing something repeatedly.

That's not entirely correct. 0^0=1 is also 1 if it's the base, and not the exponent that's changing.