# Tagged Questions

155 views

### Is this definition of limit at infinity of complex functions correct?

In my book (Churchill), a limit of a function at infinity is defined as: $$\lim\limits_{z \to \infty}f(z) \equiv \lim\limits_{z \to 0}f(\frac{1}{z})$$ But why can't you define the point at infinty ...
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### What is $\lim_{x=0\rightarrow1}x^\infty$?

I know it's all about definition... But still I want to know whether the answer is $0$, $1$, impossible to say or something else, like that the mathematical statement is wrong. However, to clarify, ...
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### Is ∞ considered defined?

$\infty$ (Infinity) is not a number, but infinity is considered to be defined, right? There are expressions in mathematics such as: $\frac x0,0^0, \frac\infty\infty,$ which are not defined because ...
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### Are distinctions in definitions of “finite” material in, eg, topology or measure theory?

There are several definitions of "finite", like Dedekind's and Tarski's (Thanks to A.K. for point out the latter - first time I've heard of it): From the Wikipedia entry on Finite Set: (Richard ...
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### What exactly is infinity?

On Wolfram|Alpha, I was bored and asked for $\frac{\infty}{\infty}$ and the result was (indeterminate). Another two that give the same result are $\infty ^ 0$ and ...
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### What is the definition of $\infty$

I saw in a note that say $\infty$ is not a real number, and there is no interval of the form $(a, \infty]$? So what is the definintion of $\infty$?
### How to define $-\infty$?
I think I understand the fundamental concept of infinity. Elementary mathematics define $\infty := \frac{x}{0}$, for every $x$. And also $\infty := \frac{-x}{0}$ for every $x$. I know only one ...