User Tristan Batchler

13 votes

4 answers

10k views

The Order of the Identity of a Group

asked May 19, 2017 at 5:49

7 votes

3 answers

227 views

$a/b < (1 + \sqrt{5})/2 \iff a^2 - ab - b^2 < 0$?

asked May 14, 2017 at 14:37

7 votes

1 answer

174 views

Why the order of elements of my group $\mathbb{Z}\left[\sqrt 7\right]$ under multiplication modulo prime $p$ often divide $p^2-1$

asked Mar 23, 2021 at 5:49

6 votes

1 answer

6k views

If the sum of eigenvectors is an eigenvector, then they all correspond to the same eigenvalue

asked Apr 28, 2017 at 23:43

5 votes

3 answers

101 views

Showing that $\sum\limits_{r=0}^n({1 \over r!} \sum\limits_{s=0}^{n-r}{(-1)^s \over s!}) = 1$

asked Aug 14, 2016 at 6:51

5 votes

3 answers

59 views

The $n$th derivative of $\frac{1}{5x^5 + 1}$ at $x=0$ is $0$ for all $n$ which is not a multiple of $5$?

asked May 30, 2017 at 23:51

4 votes

2 answers

771 views

Is the successor of a limit ordinal undefined? [closed]

asked Sep 4, 2017 at 10:29

3 votes

4 answers

164 views

What is wrong with this "proof"? $1$ is always an eigenvalue for $I + A$ ($A$ is nilpotent)?

asked May 10, 2017 at 12:07

2 votes

2 answers

110 views

Does $h \circ f = I = f \circ g \implies h = g$?

asked Mar 10, 2017 at 7:15

2 votes

0 answers

471 views

Is This Proof Valid? - $\sum_{k=1}^{n}\mu(k!)=1$ for $n \geq 3$

asked Aug 25, 2016 at 12:15

2 votes

1 answer

3k views

When to Use L'Hôpital's Rule

asked Oct 27, 2015 at 7:02

2 votes

1 answer

178 views

How can I show $z^2 = 6x^2 + 2y^2$ has no non-trivial integer solutions?

asked Oct 3, 2017 at 7:04

2 votes

3 answers

1k views

Proof that operations of $V/W$ are well defined?

asked Apr 25, 2017 at 23:57

2 votes

1 answer

1k views

Proof of Root Test?

asked May 21, 2017 at 4:10

1 vote

0 answers

980 views

Deletion-Contraction to Find Number of Spanning Trees, $\tau(G)$.

asked Aug 8, 2017 at 5:19

1 vote

3 answers

615 views

Is the order of quantifiers important in this FOL sentence?

asked Oct 24, 2017 at 1:47

1 vote

0 answers

46 views

Trying to find a function that converts a binary sequence to a number

asked Oct 25, 2017 at 13:00

1 vote

1 answer

221 views

When is the $\mu$ operator a partial function vs. total?

asked Nov 12, 2017 at 0:51

1 vote

1 answer

111 views

Maximal Directed Graph in Well-Foundedness and Extensionality?

asked Aug 19, 2017 at 8:47

1 vote

2 answers

41 views

Definitions of a Factor Surrounding $0 | 0$

asked Nov 8, 2015 at 14:07

1 vote

2 answers

3k views

Is there a bijection from $\mathbb{Q} \to \mathbb{Q} \times \mathbb{Q}$?

asked Nov 9, 2015 at 1:29

1 vote

1 answer

209 views

Prove a Function $f: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R} \times \mathbb{R}$ is Injective

asked Oct 5, 2015 at 6:36

1 vote

2 answers

813 views

$\sup{A} = \inf{B} \iff \forall \epsilon > 0, \, \exists a \in A, \, b \in B \, : \, b - a < \epsilon$

asked May 7, 2017 at 2:30

0 votes

0 answers

51 views

Let $S\in \mathcal{L} (V, W)$. Proof of $[S^]_{\beta^}^{\gamma^*} = ([S]_\gamma^\beta)^T$?

asked May 10, 2017 at 5:58

0 votes

1 answer

1k views

Is the set of linear transformations $\mathcal{L}(V, \mathbb{F})$ guaranteed to contain at least one injective transformation?

asked May 11, 2017 at 3:46

0 votes

1 answer

241 views

Is this a valid proof? (Cosets of vector subspaces)

asked Apr 25, 2017 at 5:24

0 votes

1 answer

57 views

Why is $\sum_{i=1}^n {\frac{1}{(n+i-1)(n+i)}} = \frac{1}{2n}$?

asked May 1, 2017 at 5:07

0 votes

0 answers

66 views

Showing $\int_a^b f \geq 0$ if $f$ is integrable on $[a, b]$ and $f(x) \geq 0$ $\forall x \in [a, b]$.

asked May 1, 2017 at 10:36

0 votes

1 answer

109 views

Proof Using Faraday's Law and Ampere's Law

asked Nov 1, 2016 at 1:25

0 votes

2 answers

160 views

Orbits of the Group Action from the Group of all $2 \times 2$ Diagonal non-zero Matrices on $\mathbb{R}^2$

asked Aug 29, 2016 at 2:13

Stack Exchange Network

36 Questions

The Order of the Identity of a Group

$a/b < (1 + \sqrt{5})/2 \iff a^2 - ab - b^2 < 0$?

Why the order of elements of my group $\mathbb{Z}\left[\sqrt 7\right]$ under multiplication modulo prime $p$ often divide $p^2-1$

If the sum of eigenvectors is an eigenvector, then they all correspond to the same eigenvalue

Showing that $\sum\limits_{r=0}^n({1 \over r!} \sum\limits_{s=0}^{n-r}{(-1)^s \over s!}) = 1$

The $n$th derivative of $\frac{1}{5x^5 + 1}$ at $x=0$ is $0$ for all $n$ which is not a multiple of $5$?

Is the successor of a limit ordinal undefined? [closed]

What is wrong with this "proof"? $1$ is always an eigenvalue for $I + A$ ($A$ is nilpotent)?

Does $h \circ f = I = f \circ g \implies h = g$?

Is This Proof Valid? - $\sum_{k=1}^{n}\mu(k!)=1$ for $n \geq 3$

When to Use L'Hôpital's Rule

How can I show $z^2 = 6x^2 + 2y^2$ has no non-trivial integer solutions?

Proof that operations of $V/W$ are well defined?

Proof of Root Test?

Deletion-Contraction to Find Number of Spanning Trees, $\tau(G)$.

Is the order of quantifiers important in this FOL sentence?

Trying to find a function that converts a binary sequence to a number

When is the $\mu$ operator a partial function vs. total?

Maximal Directed Graph in Well-Foundedness and Extensionality?

Definitions of a Factor Surrounding $0 | 0$

Is there a bijection from $\mathbb{Q} \to \mathbb{Q} \times \mathbb{Q}$?

Prove a Function $f: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R} \times \mathbb{R}$ is Injective

$\sup{A} = \inf{B} \iff \forall \epsilon > 0, \, \exists a \in A, \, b \in B \, : \, b - a < \epsilon$

Let $S\in \mathcal{L} (V, W)$. Proof of $[S^]_{\beta^}^{\gamma^*} = ([S]_\gamma^\beta)^T$?

Is the set of linear transformations $\mathcal{L}(V, \mathbb{F})$ guaranteed to contain at least one injective transformation?

Is this a valid proof? (Cosets of vector subspaces)

Why is $\sum_{i=1}^n {\frac{1}{(n+i-1)(n+i)}} = \frac{1}{2n}$?

Showing $\int_a^b f \geq 0$ if $f$ is integrable on $[a, b]$ and $f(x) \geq 0$ $\forall x \in [a, b]$.

Proof Using Faraday's Law and Ampere's Law

Orbits of the Group Action from the Group of all $2 \times 2$ Diagonal non-zero Matrices on $\mathbb{R}^2$