26 Can a nowhere continuous function have a connected graph? 7 Every continuous function is uniformly continuous $\Rightarrow$ Lebesgue number exists for every open cover 6 Understanding Ceva's Theorem 5 With the condition $\lim_{x\to\infty}(f(x+a)−f(x))=0$, how to prove that $f(x)$ is uniformly continuous? 5 Nonhomeomorphic subsets of the plane

### Reputation (4,503)

 -2 Prove $\lim_{n\to \infty} \sum_{k=0}^{n} 2^{\frac{-kn}{k+n}}=2$ +10 Numbers of distinct values obtained by inserting $+ - \times \div ()$ in $\underbrace{2\quad2 \quad2 \quad2\quad...\quad 2}_{n \text{ times}}$ +10 With the condition $\lim_{x\to\infty}(f(x+a)−f(x))=0$, how to prove that $f(x)$ is uniformly continuous? +10 Exercise on constructible universe: computing the L-rank of Th(HF)

### Questions (43)

 25 Numbers of distinct values obtained by inserting $+ - \times \div ()$ in $\underbrace{2\quad2 \quad2 \quad2\quad...\quad 2}_{n \text{ times}}$ 22 How well-studied is origami field theory? 16 Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite? 16 Theorems in the form of "if and only if" such that the proof of one direction is extremely EASY to prove and the other one is extremely HARD [closed] 14 A more natural solution to finding the general terms of a recurrence relation in $2$ variables

### Tags (91)

 80 general-topology × 74 7 geometry × 8 17 metric-spaces × 7 7 triangles × 4 15 real-analysis × 13 7 uniform-continuity 14 proof-explanation × 7 6 reference-request × 5 8 calculus × 3 6 group-theory × 4

### Bookmarks (577)

 769 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) 493 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$ 464 Best Sets of Lecture Notes and Articles 434 Why does $1+2+3+\cdots = -\frac{1}{12}$? 355 'Obvious' theorems that are actually false