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I know that $\infty/\infty$ is not generally defined An example of an infinite number in $ {}^\ast \mathbb r$ is represented by the sequence $1,2,3,\ldots$. However, if we have 2 equal infinities divided by each other, would it be 1
Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics Thus both the square root of infinity and square of infinity make sense when infinity is interpreted as a hyperreal number The english word infinity derives from latin infinitas, which can be translated as unboundedness , itself derived from the greek word apeiros, meaning endless .
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?
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. 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. 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
I suppose these are the equations with infinity that are universally considered correct
∞ = ∞ ∞ + n = ∞ ∞ * n = ∞ n/∞ = 0 where n can be any possible value These equations can be rearranged to. Limits and infinity minus infinity ask question asked 5 years, 9 months ago modified 1 year, 8 months ago Any number raised to the power of infinity [closed] ask question asked 14 years, 2 months ago modified 7 years, 2 months ago
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