I would say that is undefined.infinity^0 = 1?
Since 1^N == 1, then lim 1^N as N->inf is still 1. I'd argue that it might be well defined.1^infinity = 1?
The general practice is when infinity crops up as an answer you should not reduce to infinity, because after later operations the quantity may become finite again. You can see how 0/0, 1/0, and 2/0 are three different infinite values. If (1/0 = infinity) does (infinity* 0 = 1) it does not, but (1/0 *0 =1) is true.
It's similiar to how irrational numbers have infintie decimal places yet all irrational numbers are not equal. If we think about the irrational numbers as a fraction then the numerator would be one infinite number and the denomator a different one.
infinity^0 = 1?
1^infinity = 1?
Are these identities valid or a meaningless and must be associated with a context(and are meaningless anyway)?