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I know that $\infty/\infty$ is not generally defined Multiplying 0 by infinity is the equivalent of 0/0 which is undefined. 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 When you allow things like that in proofs you end up with nonsense like 1 = 0 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?
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 plus infinity ask question asked 13 years, 7 months ago modified 6 months ago Infinity divided by infinity ask question asked 7 years, 10 months ago modified 7 years, 10 months ago
For infinity, that doesn't work Under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$ 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. 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
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. Because multiplying by infinity is the equivalent of dividing by 0
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