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Bookmark or Share- mathematical operations with infinity - Mathematics Stack ExchangeLet us follow the convention that an expression with $\infty$ is "defined" (in the extended reals) if: when you replace each $\infty$ with any function/sequence whose limit is $\infty$, and each real number with any function/sequence with that limit, the limit of the entire expression is always the same real number or divergence to $\infty$ or $-\infty$.
- 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.
- 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 $1,2,3,\ldots$.
- limits - Infinity divided by infinity - Mathematics Stack ExchangeWhen we use straightforward approach, we get $$ \frac{\infty+1}{\infty} = \frac{\infty}{\infty} $$ In the process of investigating a limit, we know that both the numerator and denominator are going to infinity.. but we dont know the behaviour of each dynamics. But if we investigate further we get : $$ 1 + \frac{1}{x} $$ Some other examples :
- I have learned that 1/0 is infinity, why isn't it minus infinity?As far as I am aware, when doing floating point math on most computers in most computer languages, 1.0/0.0 will yield positive infinity (-1.0/0.0 yielding negative infinity). I think this question is extremely dependent on context and usage.
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