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What is infinity divided by infinity? - Mathematics Stack Exchange I know that $\infty \infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
One divided by Infinity? - Mathematics Stack Exchange Similarly, 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
Can I subtract infinity from infinity? - Mathematics Stack Exchange Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like limn→∞(1 + x n)n, lim n → ∞ (1 + x n) n, or is it just a parlor trick for a much easier kind of limit?
Limits and infinity minus infinity - Mathematics Stack Exchange Infinity is not a number So there there is no general meaning to any "infinity arithmetic" expression , though, there is a limit theorem which can be interpreted as an infinity arithmetic expression Here's one example of such a theorem: Because of this theorem, one might argue that it is fair to "split the limits", as you say, resulting in the "infinity arithmetic" expression
Negative 1 to the power of Infinity - Mathematics Stack Exchange 0 The limit is nonexistent Since (− 1)2n + 1 = − 1 (− 1)2n = 1, raising to n where approaches infinity means that you can't define whether the result is + 1 or − 1, or anything else, for thar matter
Is $0^\\infty$ indeterminate? - Mathematics Stack Exchange Is a constant raised to the power of infinity indeterminate? I am just curious Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
definition - Is infinity a number? - Mathematics Stack Exchange For infinity, that doesn't work; under any reasonable interpretation, 1 + ∞ = 2 + ∞ 1 + ∞ = 2 + ∞, but 1 ≠ 2 1 ≠ 2 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