The english word infinity derives from latin infinitas, which can be translated as unboundedness , itself derived from the greek word apeiros, meaning endless . I know that $\infty/\infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1 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 $1\ne2$ 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 does not lead to contradiction, but we can not conceptualize $\infty$ as a number Infinity plus infinity ask question asked 13 years, 8 months ago modified 7 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
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 divided by infinity ask question asked 7 years, 11 months ago modified 7 years, 11 months ago
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