Richard Clare

top accounts reputation activity bookmarks subscriptions

Let $f$ be continuous on $[-1,1]$, Show that $g_n \to f$ uniformly on $[-1,1]$

real-analysis measure-theory continuity uniform-convergence asked Aug 14 '17 at 20:05

math.stackexchange.com

9 votes

Let $(p_n)_{n \in \mathbb{N}}$ be the sequence of prime numbers, then $\lim_{n \to \infty}\frac{p_{n+1}}{p_n} = 1$?

number-theory elementary-number-theory prime-numbers asked Apr 15 '17 at 1:49

math.stackexchange.com

8 votes

How can I compute the discriminant of the field $\mathbb{Q}(\sqrt[3]{28})$?

abstract-algebra field-theory extension-field integral-extensions asked Jun 14 '18 at 16:06

math.stackexchange.com

7 votes

$\int_{0}^{\frac{\pi}{2}}\frac{d\theta}{a + \sin^2(\theta)} = \frac{\pi}{2\sqrt{a(a+1)}}$, for $a > 0$

calculus integration definite-integrals trigonometric-integrals asked Jul 30 '17 at 20:14

math.stackexchange.com

6 votes

How many roots has the polynomial $z^{2015} + 8z^{12} + 1$ in $\{z \in \mathbb{C}: \Im(z) > 0$ and $\Re(z) > 0\}$?

complex-analysis polynomials roots rouches-theorem asked Aug 22 '17 at 21:47

math.stackexchange.com

6 votes

Show that if $f: [0,1]\to \mathbb{R}$ is lower semi-continuous then attains its minimum on $[0,1]$

real-analysis continuity asked Aug 31 '17 at 21:52

math.stackexchange.com

5 votes

Prove that the series $\sum_{n=1}^{\infty}\int_{n}^{n+1}(\frac{1}{n^z} - \frac{1}{x^z})dx$ converges uniformly on $\mathbb{C}_{\epsilon}$

complex-analysis uniform-convergence riemann-zeta analyticity asked Jan 11 '18 at 1:54

math.stackexchange.com

5 votes

Is there any algebraic structure in the set of all continuous pdf's in $\mathbb{R}^n$ under some operation?

abstract-algebra probability-theory statistics probability-distributions asked Mar 28 '17 at 18:13

math.stackexchange.com

5 votes

Any set of positive Lebesgue measure, have a Lebesgue measurable PROPER subset with the same measure?

real-analysis measure-theory lebesgue-integral lebesgue-measure asked Aug 22 '17 at 13:17

math.stackexchange.com

current community

your communities

more stack exchange communities

Stack Exchange

Richard Clare

Let $f$ be continuous on $[-1,1]$, Show that $g_n \to f$ uniformly on $[-1,1]$

Let $(p_n)_{n \in \mathbb{N}}$ be the sequence of prime numbers, then $\lim_{n \to \infty}\frac{p_{n+1}}{p_n} = 1$?

How can I compute the discriminant of the field $\mathbb{Q}(\sqrt[3]{28})$?

$\int_{0}^{\frac{\pi}{2}}\frac{d\theta}{a + \sin^2(\theta)} = \frac{\pi}{2\sqrt{a(a+1)}}$, for $a > 0$

How many roots has the polynomial $z^{2015} + 8z^{12} + 1$ in $\{z \in \mathbb{C}: \Im(z) > 0$ and $\Re(z) > 0\}$?

Show that if $f: [0,1]\to \mathbb{R}$ is lower semi-continuous then attains its minimum on $[0,1]$

Prove that the series $\sum_{n=1}^{\infty}\int_{n}^{n+1}(\frac{1}{n^z} - \frac{1}{x^z})dx$ converges uniformly on $\mathbb{C}_{\epsilon}$

Is there any algebraic structure in the set of all continuous pdf's in $\mathbb{R}^n$ under some operation?

Any set of positive Lebesgue measure, have a Lebesgue measurable PROPER subset with the same measure?