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I know that $\infty/\infty$ is not generally defined Limits and infinity minus infinity ask question asked 5 years, 8 months ago modified 1 year, 7 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? 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. 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 .
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 divided by infinity ask question asked 7 years, 10 months ago modified 7 years, 10 months ago 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 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.
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 For infinity, that doesn't work Under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$
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