zero to the power zero

The proof is incorrect due to wrong concepts. Confusion has been made between [ lim(n→0^+) ] and [ n = 0 ]。

[ lim(n→0^+) ] represents a positive number which tends to zero, and n is NOT equal to 0. On that other hand, [ n = 0 ] shows that n is exactly equal to zero.

Note that:
lim(n→0^+) c/n = ∞, where c is a constant.
but c/0 = undefined

2011-03-14 06:00:47 補充：
If 0^0 is defined, 0^0 = any number.

Proof:

0 = 0 x (any number)
0/0 = any number ...... (*)

0^0 = 0^(1 - 1)
0^0 = 0^1/0^1
0^0 = 0/0 ...... (#)

Put (*) into (#):
0^0 = any number