Question

Show that if $f$ is growing and bounded on $(a,b)$ than $\lim\limits_{x\searrow a}f$ and $\lim\limits_{x\nearrow b}f$ exist

score 31 · Answer 1 · 2026-04-16 05:06:49

31

Views

Show that if $f$ is growing and bounded on $(a,b)$ than $\lim\limits_{x\searrow a}f$ and $\lim\limits_{x\nearrow b}f$ exist

Published on 16 Apr 2026 - 5:06

score 859 · Answer 2 · 2026-04-15 20:20:37

859

Views

Prove that for all sets A and B, A ⊆ A∪B.

Published on 15 Apr 2026 - 20:20

score 64 · Answer 3 · 2026-04-11 01:25:03

64

Views

Are the cardinalities equal?

Published on 11 Apr 2026 - 1:25

score 102 · Answer 4 · 2026-04-15 14:44:30

102

Views

$f(x - f(y))= f(f(y)) - 2xf(y) + f(x)$

Published on 15 Apr 2026 - 14:44

score 96 · Answer 5 · 2026-04-14 22:55:21

96

Views

Prove that $\lim_{n\to\infty}(n!)^\frac1n=+\infty.$

Published on 14 Apr 2026 - 22:55

score 67 · Answer 6 · 2026-04-13 00:34:31

67

Views

Is the ideal $I=(t^2+1)$ of $\mathbb{Z}[t]$ prime or maximal?

Published on 13 Apr 2026 - 0:34

score 448 · Answer 7 · 2026-04-14 18:04:31

448

Views

Find all positive integers $n$ for which $s(n)=5$.

Published on 14 Apr 2026 - 18:04

score 56 · Answer 8 · 2026-04-14 06:50:24

56

Views

Let $a > 1$ and $x > 0$. Prove that $a^x > 1$

Published on 14 Apr 2026 - 6:50

score 88 · Answer 9 · 2026-04-16 21:00:07

88

Views

Show for a monotonic function $f$ on $(a,b)$ is $\omega_f(x_0)=|\lim\limits_{x \searrow x_0}f(x)-\lim\limits_{x \nearrow x_0}f(x)|$

Published on 16 Apr 2026 - 21:00

score 276 · Answer 10 · 2026-04-15 21:26:50

276

Views

Counting ordered pairs $(a,b)$ satisfying $a^2+b^2=(a+b)^2$, with $a$ and $b$ in the interval $[-100,100]$

Published on 15 Apr 2026 - 21:26

score 119 · Answer 11 · 2026-03-25 17:21:37

119

Views

number of paths in the Cartesian plane which don't intersect the line $y = x+1/2$

Published on 25 Mar 2026 - 17:21

score 31 · Answer 12 · 2026-04-14 05:42:05

31

Views

Given an embedding $f$ on a compact, $\exists\eta>0$ such that every mapping $\eta$-close to $f$ is embedding on some smaller set.

Published on 14 Apr 2026 - 5:42

score 146 · Answer 13 · 2026-04-15 07:22:40

146

Views

If $A$ is finite and $f: A \rightarrow A$, $f$ is injective iff $\text{ran}f = A$: How Simple is My Proof Allowed to Be?

Published on 15 Apr 2026 - 7:22

score 76 · Answer 14 · 2026-04-16 16:51:05

76

Views

In which types of rings does the equality $(a)(b)=(a) \cap (b)$ hold for all $a,b$? What properties must a ring have so that this equality holds?

Published on 16 Apr 2026 - 16:51

score 53 · Answer 15 · 2026-04-11 13:09:09

53

Views

Which statements are equivalences and which are implications?

Published on 11 Apr 2026 - 13:09

List Question

Show that if $f$ is growing and bounded on $(a,b)$ than $\lim\limits_{x\searrow a}f$ and $\lim\limits_{x\nearrow b}f$ exist

Prove that for all sets A and B, A ⊆ A∪B.

Are the cardinalities equal?

$f(x - f(y))= f(f(y)) - 2xf(y) + f(x)$

Prove that $\lim_{n\to\infty}(n!)^\frac1n=+\infty.$

Is the ideal $I=(t^2+1)$ of $\mathbb{Z}[t]$ prime or maximal?

Find all positive integers $n$ for which $s(n)=5$.

Let $a > 1$ and $x > 0$. Prove that $a^x > 1$

Show for a monotonic function $f$ on $(a,b)$ is $\omega_f(x_0)=|\lim\limits_{x \searrow x_0}f(x)-\lim\limits_{x \nearrow x_0}f(x)|$

Counting ordered pairs $(a,b)$ satisfying $a^2+b^2=(a+b)^2$, with $a$ and $b$ in the interval $[-100,100]$

number of paths in the Cartesian plane which don't intersect the line $y = x+1/2$

Given an embedding $f$ on a compact, $\exists\eta>0$ such that every mapping $\eta$-close to $f$ is embedding on some smaller set.

If $A$ is finite and $f: A \rightarrow A$, $f$ is injective iff $\text{ran}f = A$: How Simple is My Proof Allowed to Be?

In which types of rings does the equality $(a)(b)=(a) \cap (b)$ hold for all $a,b$? What properties must a ring have so that this equality holds?

Which statements are equivalences and which are implications?

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