I had a thought...

[Mirinee]

*Resists urge to post*...
*Fails*

Okay, firstly, I'm sorry for hijacking your thread, adrian, but I feel that people need to know the truth.

"Zero to the power of zero is unity" hurts my brain, but it's probably true, and it will hurt my brain a lot if you try to prove it.

Forge is right-- I think whiteninja meant to say that 1 is 'not counted as a prime number', (1 will always be an odd number).

Yes, it is indeed infinity when something divides by zero, which is undefined, and that's why it's called undefined .

An even power of any number is even

An even power of any number needs not be even:
e.g. 5^2=25 (25 is odd), but any integer power of an even number is even.

wheras an odd power of a positive number is positive and a of a negative is negative

All true. In fact, any positive power of a positive number is positive.

Negative number to an odd power example:
(-2)^3 = -8 (is negative)

The square roots of all negative numbers are imaginary, as are I think cubed roots, fourthed roots, fifthed roots, etc.

If you look at the previous example, you'll notice that the odd number roots of a negative number are not imaginary: they are negative.

e.g.
(-8)^(1/3) = -2 (Cube root of -8 is -2, which is not imaginary. Don't ask your calculator to verify this. It won't know. Ask FOmar.)