Something I should remember but can't! What do numbers to the power of Zero equal? To the power of one they are themselves and squared, cubed etc is obvious but zero?? Anyone remember

Printable View

- Jun 12th 2006, 08:04 PMGini[SOLVED] Power of Zero
Something I should remember but can't! What do numbers to the power of Zero equal? To the power of one they are themselves and squared, cubed etc is obvious but zero?? Anyone remember

- Jun 12th 2006, 08:20 PMmalaygoelQuote:

Originally Posted by**Gini**

- Jun 12th 2006, 08:21 PMCaptainBlackQuote:

Originally Posted by**malaygoel**

RonL - Jun 13th 2006, 10:23 AMThePerfectHackerQuote:

Originally Posted by**CaptainBlack**

In England that is not the style though. - Jun 13th 2006, 04:34 PMQuickQuote:

Originally Posted by**ThePerfectHacker**

$\displaystyle a^3 \cdot a^{-3} = a^{(3-3)} = a^0 = 1 $

or it could be written as...

$\displaystyle a^3 \cdot a^{-3} = \frac{a^3}{a^3} = 1 $

so $\displaystyle 0^1 \cdot 0^{-1} = 0^{(1-1)} = 0^0 = $undefined

or it could be written as...

so $\displaystyle 0^1 \cdot 0^{-1} = \frac{0^1}{0^1} = \frac{0}{0} = $ undefined - Jun 13th 2006, 04:51 PMThePerfectHackerQuote:

Originally Posted by**Quick**

This is my 14:):)th Post!!! - Jun 13th 2006, 09:07 PMJakeDQuote:

Originally Posted by**Quick**

- Jun 14th 2006, 02:34 AMQuickQuote:

Originally Posted by**JakeD**

- Jun 14th 2006, 04:37 AMCaptainBlackQuote:

Originally Posted by**Quick**

if/when the convention of it being undefined is changed.

RonL - Jun 14th 2006, 04:45 AMCaptainBlackQuote:

Originally Posted by**JakeD**

author defines what they want it to mean, it is ambiguous and

hence undefined :D

Quote:

This page has a good discussion and claims "Consensus has recently been built around setting the value of $\displaystyle 0^0 = 1.$"

- Jun 14th 2006, 11:57 AMtopsquarkQuote:

Originally Posted by**CaptainBlack**

$\displaystyle \lim_{x \to 0}0^x \to 0$

and

$\displaystyle \lim_{y \to 0}y^0 \to 1$

As the limits do not agree we can't say that $\displaystyle 0^0$ is defined. What confuses me is why there is even discussion about defining it to be one or the other?? :confused:

-Dan - Jun 14th 2006, 12:06 PMTD!
Have you thought of letting x approach 0 as base and power symmetrically?

$\displaystyle \mathop {\lim }\limits_{x \to 0} x^x = 1$

This should make the "convention" at least more plausible. - Jun 14th 2006, 12:06 PMQuickQuote:

Originally Posted by**topsquark**

**UNDEFINED**

I also think this post should be moved to chat room or miscellaneous.