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I know that $\infty/\infty$ is not generally defined So while for some purposes it is useful to treat infinity as if it were a number, it is important to remember that it won't always act the way you've become accustomed to expect a number to act. However, if we have 2 equal infinities divided by each other, would it be 1

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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? Under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$ 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.

Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics The english word infinity derives from latin infinitas, which can be translated as unboundedness , itself derived from the greek word apeiros, meaning endless . 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 Infinity divided by infinity ask question asked 7 years, 9 months ago modified 7 years, 9 months ago Limits and infinity minus infinity ask question asked 5 years, 8 months ago modified 1 year, 6 months ago I understand that there are different types of infinity

One can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers

7 neither the maximum or supremum of a subset are guaranteed to exist If you consider the real numbers as a subset of itself, there is no supremum If you consider it a subset of the extended real numbers, which includes infinity, then infinity is the supremum. For infinity, that doesn't work