Can we include $\infty$ and $1/\infty$ into $\mathbb R$?
47871
Why did mathematician construct extended real number systems, $\mathbb R \cup\{+\infty,-\infty\}$?
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
127627
Does $\sum^{\infty}_{n=1} n/(n-1)!$ converge to something?
79419
Is $\sin \infty$ an indeterminate form?
25646
What is the result of $\infty - \infty$?
53688
How can one prove that $\lim_{n \to \infty}a^{1/n}=1$ for every $a>0$?
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
119804
If $\lim_{n\to \infty}a_n = a\in \mathbb{R}$ . Prove that $\limsup_{n\to \infty}a_n x_n=a\limsup_{n\to \infty}x_n$ .
26338
Does $1^{\infty}=e$ or $1^{\infty}=1$?
158011
$C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
153697
Is there a function $f: \mathbb{R} \to \mathbb{R}$ such that $\lim\limits_{x\to p}f(x)=\infty$ for every $p \in \mathbb{R}$
147887
When do we have $ \lim_{n\to\infty}\sum_{k=1}^{n^2}\frac{n^{r-1}}{n^r+k^r}0$?
50673
Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
84830
Vector space of infinite sequences in $\Bbb R$
145471
$\Gamma \subset \mathbb{R}^{+}$ is uncountable. Can we choose a sequence from $\Gamma$ of which the sum is $\infty$
142778
Finding $\lim_{n\to\infty}a_n$ if $a_0=a,a_1=b$ and $a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$ where $a, b \in \mathbb{R}$