Anything to the power of 1 is that same something, so infinity to the power of 1 is infinity. Keep in mind that infinity is a conceptual thing, often expressed as a limit as something approaches a boundary condition of the domain of a function. Without thinking of limits, infinity squared is still infinity, so the normal rules of math would seem to not apply.
E to the power infinity, or lim en as n approaches infinity is infinity.
Also infinity. If you are concerned about the size of sets, it is a higher-level (larger) infinity. For example, 2 to the power aleph-zero, or aleph-zero to the power aleph-zero, is equal to aleph-one.
The answer is not 1. While it may seem like 1 raised to anything equals 1 (because 1x1=1, and 1x1x1=1, ad infinitum), this is actually not the case. The answer is that 1 raised to infinity is indeterminate. When dealing with infinity, you are talking about a non-finite number, so that essentially throws all rules about algebra out the window.
???
infinity
10 (or e) to the power of x range from zero to infinity. Lets try the extreme cases: 10^infinity = infinity 10^0 = 1 10^-infinity = 1/infinity = 0
E to the power infinity, or lim en as n approaches infinity is infinity.
Infinity.
11=11=!1=11...=1
Infinity.
Infinity.
Yes. The rule is used to find the limit of functions which are an indeterminate form; that is, the limit would involve either 0/0, infinity/infinity, 0 x infinity, 1 to the power of infinity, zero or infinity to the power of zero, or infinity minus infinity. So while it is not used on all functions, it is used for many.
Infinity
Infinity.
infinity
The infinity symbol is ∞, if this is what you are asking.
Also infinity. If you are concerned about the size of sets, it is a higher-level (larger) infinity. For example, 2 to the power aleph-zero, or aleph-zero to the power aleph-zero, is equal to aleph-one.