Error 404

 11 Greatest value of $\frac{1}{4\sin \theta-3 \cos \theta+6}$ 8 Example of continuous mapping of open(closed) set to not open(closed) set 4 Closed property of nonempty finite set 4 How to prove this statement with “first” principle of Mathematical induction and not strong Mathematical induction? 4 Find the sum of this series?

### Reputation (3,983)

 +10 Showing that a harmonic function maps open sets to open sets. +5 Describing automorphisms of a punctured unit disc +5 Let $C$ be a space such that $C=A \cup B$ and $A \cap B ↪ A$ is a cofibration. Show that $B ↪C$ is a cofibration. +5 Let $S=[0,1) \cup [2,3]$ and $f:S \to \Bbb R$ be a strictly increasing map such that $f(S)$ is connected. Which of the following statements is true?

### Questions (108)

 17 Can we have a one-one function from [0,1] to the set of irrational numbers? 13 Calculating number of equivalence classes where two points are equivalent if they can be joined by a continuous path. 9 Let $f: \Bbb R \to \Bbb R$ be a differentiable function such that $\sup_{x \in \Bbb R}|f'(x)| \lt \infty$. Then 8 How to use generalized pigeonhole principle to be sure that at least one of the integers picked is even? 8 Let $f: \Bbb R \to \Bbb R$ be a continuously differentiable function such that $|f(x)-f(y)| \ge |x-y| \forall x,y \in \Bbb R$ Then $f'(x)=\frac 12$

### Tags (157)

 44 real-analysis × 55 15 continuity × 21 22 algebra-precalculus × 7 15 abstract-algebra × 17 21 sequences-and-series × 25 15 limits × 16 20 calculus × 17 14 trigonometry × 7 17 general-topology × 20 13 elementary-set-theory × 13

### Accounts (39)

 Mathematics 3,983 rep 21436 Physics 121 rep 2 Android Enthusiasts 106 rep 12 MathOverflow 101 rep 1 English Language Learners 101 rep 1