Question

Prove that a strictly increasing function $f:[a,b]\rightarrow\mathbb{R}$ which has the intermediate value property is coninuous on $[a,b]$.

score 1k · Answer 1 · 2015-12-06 06:57:52

Prove that a strictly increasing function $f:[a,b]\rightarrow\mathbb{R}$ which has the intermediate value property is coninuous on $[a,b]$.

score 130 · Answer 2 · 2015-12-07 18:16:47

130

Views

Show that $\int_1^\infty \frac{\ln x}{\left(1+x^2\right)^\lambda}\mathrm dx$ is convergent only for $\lambda > \frac{1}{2}$

Published on 07 Dec 2015 - 18:16

score 4.3k · Answer 3 · 2015-12-07 20:56:22

4.3k

Views

n-cents stamp (Strong induction)

Published on 07 Dec 2015 - 20:56

score 75 · Answer 4 · 2026-04-03 00:31:39

75

Views

If $\limsup_{n\to\infty} \ x_{n} = a$ then why does it exist a subsquence $s_{n}$, which $\lim_{n\to\infty} \ s_{n} = a$?

Published on 03 Apr 2026 - 0:31

score 104 · Answer 5 · 2015-12-10 12:38:36

104

Views

Is there a shorter proof to show that this complex intergral is constant?

Published on 10 Dec 2015 - 12:38

score 108 · Answer 6 · 2015-12-12 04:17:23

108

Views

Is this a sufficient proof of a math contest problem?

Published on 12 Dec 2015 - 4:17

score 83 · Answer 7 · 2026-03-30 03:54:49

83

Views

Condition for inverse of quadratic function - alternative solutions

Published on 30 Mar 2026 - 3:54

score 366 · Answer 8 · 2026-03-25 12:29:26

366

Views

Triple Products are Isomorphic

Published on 25 Mar 2026 - 12:29

score 84 · Answer 9 · 2026-04-04 17:34:46

84

Views

Verify proof of $ f(x)=e^x $ if $ f(x+y)=f(x)f(y) $ and $ f'(x)$ exists for all $x$

Published on 04 Apr 2026 - 17:34

score 3.8k · Answer 10 · 2015-12-15 01:48:16

3.8k

Views

Prove that a group of order 25 has a subgroup of order 5

Published on 15 Dec 2015 - 1:48

score 1.1k · Answer 11 · 2015-12-15 17:54:52

1.1k

Views

Frattini subgroup of a finite elementary abelian $p$-group is trivial

Published on 15 Dec 2015 - 17:54

score 1.3k · Answer 12 · 2015-12-15 19:07:25

1.3k

Views

Proving that the preimage of an open set is open

Published on 15 Dec 2015 - 19:07

score 142 · Answer 13 · 2015-12-16 16:15:22

142

Views

Prove that if a group $G$ has $|G| = 6$ then $G$ is isomorphic to either $\Bbb Z/6$ or $S_3$

Published on 16 Dec 2015 - 16:15

score 132 · Answer 14 · 2015-12-18 07:59:41

132

Views

What is $\mathbb Q +A=\{q+a : q\in \mathbb Q , a\in A\subset [0,1]\}$ $?$

Published on 18 Dec 2015 - 7:59

score 261 · Answer 15 · 2015-12-18 18:51:30

261

Views

Are topologies on $\Bbb R$ with bases $\{[-n,n]:n\in\Bbb N\}$ and $\{(-n,n):n\in\Bbb N\}$ homeomorphic?

Published on 18 Dec 2015 - 18:51

List Question

Prove that a strictly increasing function $f:[a,b]\rightarrow\mathbb{R}$ which has the intermediate value property is coninuous on $[a,b]$.

Show that $\int_1^\infty \frac{\ln x}{\left(1+x^2\right)^\lambda}\mathrm dx$ is convergent only for $\lambda > \frac{1}{2}$

n-cents stamp (Strong induction)

If $\limsup_{n\to\infty} \ x_{n} = a$ then why does it exist a subsquence $s_{n}$, which $\lim_{n\to\infty} \ s_{n} = a$?

Is there a shorter proof to show that this complex intergral is constant?

Is this a sufficient proof of a math contest problem?

Condition for inverse of quadratic function - alternative solutions

Triple Products are Isomorphic

Verify proof of $ f(x)=e^x $ if $ f(x+y)=f(x)f(y) $ and $ f'(x)$ exists for all $x$

Prove that a group of order 25 has a subgroup of order 5

Frattini subgroup of a finite elementary abelian $p$-group is trivial

Proving that the preimage of an open set is open

Prove that if a group $G$ has $|G| = 6$ then $G$ is isomorphic to either $\Bbb Z/6$ or $S_3$

What is $\mathbb Q +A=\{q+a : q\in \mathbb Q , a\in A\subset [0,1]\}$ $?$

Are topologies on $\Bbb R$ with bases $\{[-n,n]:n\in\Bbb N\}$ and $\{(-n,n):n\in\Bbb N\}$ homeomorphic?

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