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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 14 years, 2 months ago modified 7 years, 3 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 .
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 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. 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 Infinity divided by infinity ask question asked 7 years, 11 months ago modified 7 years, 11 months ago
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. For infinity, that doesn't work Under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$
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