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Bookmark or Share- One divided by Infinity? - Mathematics Stack ExchangeSimilarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it. You can extend those sets to include infinity - but then you have to extend the definition of the arithmetic operators, to cope with that extended set. And then, you need to start thinking about arithmetic differently.
- Why is $\\infty\\times 0$ indeterminate? - Mathematics Stack ExchangeYour title says something else than "infinity times zero". It says "infinity to the zeroth power". It is also an indefinite form because $$\infty^0 = \exp(0\log \infty) $$ but $\log\infty=\infty$, so the argument of the exponential is the indeterminate form "zero times infinity" discussed at the beginning.
- What is infinity divided by infinity? - Mathematics Stack ExchangeEssentially, you gave the answer yourself: "infinity over infinity" is not defined just because it should be the result of limiting processes of different nature. I.e., since such a definition would be given for the sake of completeness and coherence with the fact "the limiting ratio is the ratio of the limits", your
- What is the square root of infinity and what is infinity^2?Thus both the "square root of infinity" and "square of infinity" make sense when infinity is interpreted as a hyperreal number. An example of an infinite number in ${}^\ast \mathbb R$ is represented by the sequence $1,2,3,\ldots$.
- calculus - Limits and infinity minus infinity - Mathematics Stack ExchangeInfinity is not a number. So there there is no general meaning to any "infinity arithmetic" expression. Sometimes, though, there is a limit theorem which can be interpreted as an infinity arithmetic expression. Here's one example of such a theorem:
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