What is infinity to the zeroth power?

Question

I am not happy with the answers posted to similar questions.

For example, in:

What is infinity to the power zero

the accepted answer is 1, which is definitely wrong.

I think the answer is any non-zero, non-one, non-infinite number. Is this correct?

Looking for the solution to: $(1/0)^0$

Answer 1

It is an indeterminate form and as such cannot be assigned any value.

It is better expressed as $\lim_\limits{{x\to \infty}\\,\\{y\to 0}}x^y$.

As commented by Did, it is true that $x^y$ has no limit when $x\to \infty$ and $y\to 0$.

And $\infty^0$ has no definite meaning in mathematics. It is basically some kind of a meaningless statement where the notation of infinity has been wrongly used since infinity is not a number, it is a concept. To speak of infinity, I must add the following:

In standard real analysis, the symbol $\infty$ is simply used to denote an unbounded limit. Whenever the symbol is used, in series and integrals, for example, it has a precise definition with epsilon/delta. Similarly, in set theory, it also has a precise definition; we say a set $S$ is infinite if there is no bijection from $S$ to a bounded subset of $\mathbb{N}$.