Question

Prove $(\forall x, y \in E)(\exists ! z\in Z)$ s. t. $x + z = y$.

score 293 · Answer 1 · 2026-04-15 12:24:59

293

Views

Prove $(\forall x, y \in E)(\exists ! z\in Z)$ s. t. $x + z = y$.

Published on 15 Apr 2026 - 12:24

score 136 · Answer 2 · 2026-04-16 12:00:40

136

Views

Prove that for all sets $A$ and $B$ $A\subseteq B$ implies $A\cap B=A$.

Published on 16 Apr 2026 - 12:00

score 1.1k · Answer 3 · 2026-04-11 16:24:52

1.1k

Views

Show a continuous function $f$ attains a maximum value in $\Bbb{R}$.

Published on 11 Apr 2026 - 16:24

score 84 · Answer 4 · 2026-04-15 13:02:52

84

Views

Show that $a_n:=\frac{(-1)^{n-1}}{2n-1}$ converges

Published on 15 Apr 2026 - 13:02

score 232 · Answer 5 · 2026-04-11 15:31:36

232

Views

Review of Proof of DeMorgan’s law for sets

Published on 11 Apr 2026 - 15:31

score 173 · Answer 6 · 2026-04-15 12:12:30

173

Views

Please check: $f:X\longrightarrow Y$ perfect map. Let $X$ be second countable, prove $Y$ is second countable

Published on 15 Apr 2026 - 12:12

score 257 · Answer 7 · 2026-04-16 14:03:55

257

Views

$\sup(a + B) = a + \sup B$

Published on 16 Apr 2026 - 14:03

score 742 · Answer 8 · 2026-04-12 06:43:50

742

Views

Proof checking $\liminf cx_n = c \limsup x_n$

Published on 12 Apr 2026 - 6:43

score 113 · Answer 9 · 2026-04-15 21:08:17

113

Views

To prove the existence of solution(s) of $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=4$

Published on 15 Apr 2026 - 21:08

score 172 · Answer 10 · 2026-04-13 03:44:58

172

Views

Show the ideal $(x-2,x+3)\subset\mathbb{Z}[x]$ is prime but not principal

Published on 13 Apr 2026 - 3:44

score 143 · Answer 11 · 2026-04-13 04:39:50

143

Views

Showing a vector field isn't conservative without using a contour integral

Published on 13 Apr 2026 - 4:39

score 73 · Answer 12 · 2026-04-16 17:22:50

73

Views

Find $a$ so that $\max{(1-2x, y)}$ < a and $\max{(1-2y, x)} < a$ are independent

Published on 16 Apr 2026 - 17:22

score 76 · Answer 13 · 2026-04-17 05:31:42

76

Views

$f(x+1) = f(x)$ for all $x ∈ \mathbb{R}$. Let $g(t)=\int_{0}^tf(x)dx$ $h(t)=\lim_{n→\infty}\frac{g(t+n)}n, t∈\mathbb{R}$

Published on 17 Apr 2026 - 5:31

score 304 · Answer 14 · 2026-04-14 07:45:28

304

Views

Proof of "For transitive closure of a relation $R$ on a finite set with $n$ elements it is sufficient to find $R^*=\bigcup_{k=1}^n R^k$"

Published on 14 Apr 2026 - 7:45

score 243 · Answer 15 · 2026-04-12 10:31:51

243

Views

In the described game, can the rubies be divided into 105 piles of one?

Published on 12 Apr 2026 - 10:31

List Question

Prove $(\forall x, y \in E)(\exists ! z\in Z)$ s. t. $x + z = y$.

Prove that for all sets $A$ and $B$ $A\subseteq B$ implies $A\cap B=A$.

Show a continuous function $f$ attains a maximum value in $\Bbb{R}$.

Show that $a_n:=\frac{(-1)^{n-1}}{2n-1}$ converges

Review of Proof of DeMorgan’s law for sets

Please check: $f:X\longrightarrow Y$ perfect map. Let $X$ be second countable, prove $Y$ is second countable

$\sup(a + B) = a + \sup B$

Proof checking $\liminf cx_n = c \limsup x_n$

To prove the existence of solution(s) of $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=4$

Show the ideal $(x-2,x+3)\subset\mathbb{Z}[x]$ is prime but not principal

Showing a vector field isn't conservative without using a contour integral

Find $a$ so that $\max{(1-2x, y)}$ < a and $\max{(1-2y, x)} < a$ are independent

$f(x+1) = f(x)$ for all $x ∈ \mathbb{R}$. Let $g(t)=\int_{0}^tf(x)dx$ $h(t)=\lim_{n→\infty}\frac{g(t+n)}n, t∈\mathbb{R}$

Proof of "For transitive closure of a relation $R$ on a finite set with $n$ elements it is sufficient to find $R^*=\bigcup_{k=1}^n R^k$"

In the described game, can the rubies be divided into 105 piles of one?

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