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I know that $\infty/\infty$ is not generally defined Any number raised to the power of infinity [closed] ask question asked 13 years, 11 months ago modified 6 years, 11 months ago However, if we have 2 equal infinities divided by each other, would it be 1

Can this interpretation (subtract one infinity from another infinite quantity, that is twice large as the previous infinity) help us with things like $\lim_ {n\to\infty} (1+x/n)^n,$ or is it just a parlor trick for a much easier kind of limit? The english word infinity derives from latin infinitas, which can be translated as unboundedness , itself derived from the greek word apeiros, meaning endless . Infinity divided by infinity ask question asked 7 years, 8 months ago modified 7 years, 8 months ago

Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it

And then, you need to start thinking about arithmetic differently. This $1^\infty$ (in regards to indeterminate forms) actually means When there is an expression that approaches 1 and then it is raised to the power of an expression that approaches infinity we can't determine what happens in that form In particular, infinity is the same thing as 1 over 0, so zero times infinity is the same thing as zero over zero, which is an indeterminate form

Your title says something else than infinity times zero It says infinity to the zeroth power. The infinity can somehow branch in a peculiar way, but i will not go any deeper here This is just to show that you can consider far more exotic infinities if you want to

Let us then turn to the complex plane

Is a constant raised to the power of infinity indeterminate Say, for instance, is $0^\\infty$ indeterminate Or is it only 1 raised to the infinity that is? Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics

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