ramanujan

### Questions (26)

 76 Why did mathematicians introduce the concept of uniform continuity? 7 $\operatorname{Aut} (G)$ is isomorphic to $\operatorname{Aut} (H)$ then is it necessary that $G$ is isomorphic to $H$? 3 $7$ Sylow subgroup of $A_{20}$ is not normal and $7$ Sylow subgroup of $S_{20}$ contained in $A_{20}$. 3 Cartesian product of countable number of finite sets is countable. 3 If $\phi:G \to \overline G$ is group homomorphism, then prove that $|\phi(G)|$ divides $|G|$.

### Reputation (1,424)

 +30 Why did mathematicians introduce the concept of uniform continuity? +10 Is function integrable? +10 If $f,g$ are uniformly continuous prove $f+g$ is uniformly continuous but $fg$ and $\dfrac{f}{g}$ are not +10 Radius of convergence of $f(z)?$

 4 Proving $1/(2+x_n)$ is a contractive sequence and find its limit 4 If $f,g$ are uniformly continuous prove $f+g$ is uniformly continuous but $fg$ and $\dfrac{f}{g}$ are not 2 Radius of convergence of $f(z)?$ 1 Is function integrable? 1 consider $\mathbb{P}_n[x]$ and $\mathbb{P}[x]$ over $\mathbb{R}$ Is the following statement is True/ false?

### Tags (42)

 4 real-analysis × 14 4 continuity × 2 4 sequences-and-series × 5 4 epsilon-delta 4 limits × 3 2 convergence-divergence × 2 4 uniform-continuity × 3 2 complex-analysis × 2 4 proof-verification × 3 1 linear-algebra × 4