# user19038

 16h comment Proving/ Disproving that a set is compact in $l^2$Each standard unit vector, $e_i$, is in $A$. Does the sequence $(e_i)$ have a convergent subsequence? 22h comment Uniform Convergence on every bounded closed intervals implies Uniform Convergence on $\Bbb R$It's not true. Take $f_n=\chi_{[-n,n]}$. This converges to the constant function $1$ uniformly on any closed, bounded interval. 1d comment Convergence from another series$0\le(a-b)^2=a^2+b^2-2ab$. 2d awarded Guru 2d comment Continuous function rational for every point, Cantor functionIt's not rational at every point. Apr 28 comment Does convergence almost everywhere to an $L^p$ function and existence of a weakly convergent subsequence guarantee weak convergence?Here's one way to solve your problem. Apr 26 revised Let $f : (a,b) \rightarrow R$ and $x_{0} \in (a,b)$. Assume that there are real numbers $L$ and $M$ such that ...edited tags Apr 26 revised continuity of a piece wise function defined partially on a closed intervaledited tags Apr 20 answered On the dimension of a real Normed Linear Space possessing a certain property Apr 20 comment Why do so many projectile motion equation examples use $-16$ as the $a$ coefficient?It's closer to $32.174$, at sea level. Apr 19 comment On the dimension of a real Normed Linear Space possessing a certain propertyIn an infinite dimensional space $X$, take $Y$ to be the kernel of a discontinuous linear functional. This is dense in $X$ and proper; so, there is no $x\in X$ with $\text{dist}\,(x,Y)=1$. Apr 17 comment How to test the convergence of $\sum^{\infty}_{n=2}\frac{1}{\ln{n}}$ and $\sum^{\infty}_{n=2}\frac{\ln{n}}{n^{1.1}}$?\$\ln n