24 What is wrong with this argument that closed interval [0, 1] is not compact? 13 If $ab=ba$, Prove $a^2$ commutes with $b^2$ 12 Normalizing a quaternion 9 Showing planarity of graphs 8 Determining the closed form of $\sum\limits_{r = 2}^n \binom{n}{r} \binom{r}{2}$

### Reputation (7,562)

 +18 Find the missing number of the given series +10 What does it mean to converge to a point if it is not clear what the point even is? +50 Two properties of $f(x) = x \ln { (\frac{2}{\pi} \arctan{x}) }$ how do I prove these? +10 Rewriting of a complex number

### Questions (53)

 12 Ellipsoid but not quite 5 Two properties of $f(x) = x \ln { (\frac{2}{\pi} \arctan{x}) }$ how do I prove these? 4 Prove that $1-\frac{\sin(x)}{x} < x^2/2$ for $x \in (0, \pi/2)$ 4 Coefficient of $x^{27}$ in $(1-x^{10})^6/(1-x)^6$. 4 Simple problem on conditional geometric probability

### Tags (174)

 58 proof-verification × 11 31 elementary-number-theory × 17 48 real-analysis × 36 29 functions × 18 45 calculus × 50 25 general-topology × 6 40 combinatorics × 20 25 definition × 2 39 algebra-precalculus × 22 24 elementary-set-theory × 13

### Bookmarks (77)

 109 Can an infinite sum of irrational numbers be rational? 91 Best Maths Books for Non-Mathematicians [closed] 82 Can we remove any prime number with this strange process? 50 What is the antiderivative of $e^{-x^2}$ 29 A simple way to obtain $\prod_{p\in\mathbb{P}}\frac{1}{1-p^{-s}}=\sum_{n=1}^{\infty}\frac{1}{n^s}$.