Question

Prove the surjectivity of $\nu(r,m) = 2^{r+1}m + \frac{2^{r}(3-2(-1)^{r})-1}{3}$ to $2 \mathbb{N}+1$ via induction

score 41 · Answer 1 · 2026-04-15 19:05:14

41

Views

Prove the surjectivity of $\nu(r,m) = 2^{r+1}m + \frac{2^{r}(3-2(-1)^{r})-1}{3}$ to $2 \mathbb{N}+1$ via induction

Published on 15 Apr 2026 - 19:05

score 758 · Answer 2 · 2026-04-15 13:27:28

758

Views

Bijection between the power set of $\mathbb{Z}_+$ and the set of all infinite sequences $(x_n)_{n=1}^\infty$ with $x_n\in\{0,1\}$

Published on 15 Apr 2026 - 13:27

score 74 · Answer 3 · 2026-04-13 14:09:28

74

Views

Show $\begin{bmatrix}d-\lambda\cr -c\end{bmatrix}$ is eigenvector of $\begin{bmatrix}a &b\cr c&d\end{bmatrix}$

Published on 13 Apr 2026 - 14:09

score 55 · Answer 4 · 2026-04-12 19:00:37

55

Views

Is there a name for this type of word problems?

Published on 12 Apr 2026 - 19:00

score 74 · Answer 5 · 2026-04-13 14:48:53

74

Views

Prove the equivalence: $f$ is continuous on $A$ iff whenever $U$ is open in $\textbf{R}$, then $f^{-1}(U)$ is a relatively open subset of $A$.

Published on 13 Apr 2026 - 14:48

score 44 · Answer 6 · 2026-04-16 08:43:22

44

Views

Prove that the set $A = \{(x, y) \mid x$ is an odd integer and $y$ is an even integer$\}$ is enumerable

Published on 16 Apr 2026 - 8:43

score 296 · Answer 7 · 2026-04-15 08:08:26

296

Views

Show $\log(\det(A))\le \operatorname{tr}(A)-n$

Published on 15 Apr 2026 - 8:08

score 118 · Answer 8 · 2026-04-16 10:51:29

118

Views

$\int_0^\infty\frac{x^2+3}{x^4+1}\,dx$ via contour integration?

Published on 16 Apr 2026 - 10:51

score 77 · Answer 9 · 2026-04-13 04:16:06

77

Views

Proving a group homomorphism

Published on 13 Apr 2026 - 4:16

score 56 · Answer 10 · 2026-04-14 22:52:44

56

Views

$\forall x \in \mathbb{R}^+ ( \exists M \in \mathbb{Z}^+ ( x > 1/M > 0))$: Cauchy Sequences

Published on 14 Apr 2026 - 22:52

score 67 · Answer 11 · 2026-04-12 16:55:06

67

Views

Prove that $f(x)$ is non-increasing on $(0,1)$.

Published on 12 Apr 2026 - 16:55

score 426 · Answer 12 · 2026-04-16 02:57:30

426

Views

Let $f$ be an entire function such that $|f'(z)|\leq |f(z)|$ for all $z$. Show that $f(z)=ae^{cz}$

Published on 16 Apr 2026 - 2:57

score 32 · Answer 13 · 2026-04-14 20:32:40

32

Views

Determination of the value of $n$ in $\mathbb{Z}_n$ subject to $x+y=2$ and $2x-3y=3$

Published on 14 Apr 2026 - 20:32

score 112 · Answer 14 · 2026-04-16 01:14:57

112

Views

If there is a map $Y \rightarrow Z$, then there is a map $X_1 \times_Y X_2 \rightarrow X_1 \times_Z X_2$

Published on 16 Apr 2026 - 1:14

score 75 · Answer 15 · 2026-04-13 09:44:31

75

Views

Prove that $G$ is not an open set in $\mathbb R^2$

Published on 13 Apr 2026 - 9:44

List Question

Prove the surjectivity of $\nu(r,m) = 2^{r+1}m + \frac{2^{r}(3-2(-1)^{r})-1}{3}$ to $2 \mathbb{N}+1$ via induction

Bijection between the power set of $\mathbb{Z}_+$ and the set of all infinite sequences $(x_n)_{n=1}^\infty$ with $x_n\in\{0,1\}$

Show $\begin{bmatrix}d-\lambda\cr -c\end{bmatrix}$ is eigenvector of $\begin{bmatrix}a &b\cr c&d\end{bmatrix}$

Is there a name for this type of word problems?

Prove the equivalence: $f$ is continuous on $A$ iff whenever $U$ is open in $\textbf{R}$, then $f^{-1}(U)$ is a relatively open subset of $A$.

Prove that the set $A = \{(x, y) \mid x$ is an odd integer and $y$ is an even integer$\}$ is enumerable

Show $\log(\det(A))\le \operatorname{tr}(A)-n$

$\int_0^\infty\frac{x^2+3}{x^4+1}\,dx$ via contour integration?

Proving a group homomorphism

$\forall x \in \mathbb{R}^+ ( \exists M \in \mathbb{Z}^+ ( x > 1/M > 0))$: Cauchy Sequences

Prove that $f(x)$ is non-increasing on $(0,1)$.

Let $f$ be an entire function such that $|f'(z)|\leq |f(z)|$ for all $z$. Show that $f(z)=ae^{cz}$

Determination of the value of $n$ in $\mathbb{Z}_n$ subject to $x+y=2$ and $2x-3y=3$

If there is a map $Y \rightarrow Z$, then there is a map $X_1 \times_Y X_2 \rightarrow X_1 \times_Z X_2$

Prove that $G$ is not an open set in $\mathbb R^2$

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