35 Does $abab=baba$ imply commutativity in a Group of uneven order? 29 Interpretation of limsup-liminf of sets 28 Piecewise functions: Got an example of a real world piecewise function? 24 Show that $\frac{(3^{77}-1)}{2}$ is odd and composite 22 Is $\sin^2\theta + \cos\theta = 2$ solvable without a mess?

### Reputation (15,354)

 +10 Any finitely generated subgroup of $(\mathbb{Q},+)$ is cyclic. +10 Generalization of variance to random vectors +10 Any ball is connected? +10 “Antisymmetry” among cut points

### Questions (27)

 158 Is there a homology theory that counts connected components of a space? 43 Does there exist $f:(0,\infty)\to(0,\infty)$ such that $f'=f^{-1}$? 39 What is the sum of sum of digits of $4444^{4444^{4444}}$? 20 Generalization of variance to random vectors 13 Can the cardinality of continuum exceed all aleph numbers in ZF?

### Tags (126)

 171 general-topology × 48 56 connectedness × 12 137 real-analysis × 34 54 elementary-set-theory × 9 82 calculus × 17 42 algebra-precalculus × 8 75 group-theory × 9 41 elementary-number-theory × 4 62 sequences-and-series × 14 40 functional-equations × 11

### Bookmarks (2,406)

 1295 Visually stunning math concepts which are easy to explain 772 How to study math to really understand it and have a healthy lifestyle with free time? [closed] 716 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) 665 What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed] 653 Splitting a sandwich and not feeling deceived