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I know that $\infty/\infty$ is not generally defined My argument is that if $1 + \infty > \infty$ then there exists a number greater than $\infty$, disproving the concept of infinity, because you can't simply add $1$ to infinity, because infinity is ever increasing. However, if we have 2 equal infinities divided by each other, would it be 1
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Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics Infinity divided by infinity ask question asked 7 years, 10 months ago modified 7 years, 10 months ago 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?
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. 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 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.
