User pyridoxal_trigeminus

10 votes

9 answers

8k views

How to rationalize the denominator $\frac{1}{1 + \sqrt[3]{5} - \sqrt[3]{25}}$

asked May 10, 2023 at 3:36

8 votes

0 answers

677 views

Prove that $\mathbb{Z} \times\Bbb Z_2$ and $\mathbb{Z}$ are not isomorphic.

asked Jan 31, 2022 at 4:50

6 votes

3 answers

219 views

Is there a such thing as a free group generated by a free group?

asked Mar 19, 2022 at 3:20

6 votes

1 answer

155 views

How to find all positive integers $n,k$ such that ${n\choose k}=m$ for a given $m$?

asked Mar 19 at 2:36

5 votes

1 answer

177 views

Why is $2$ the doubling constant of $\mathbb R$?

asked Feb 16, 2023 at 22:28

5 votes

1 answer

101 views

Are there any topological spaces containing no proper retracts? i.e. $A\subset X$ s.t. $\exists r:X\to A$ continuous w/ $r(a)=a,\forall a\in A$

asked Aug 3, 2022 at 2:12

5 votes

1 answer

939 views

Prove that for any $x \in \mathbb{R}$, $x = \sup \{q \in \mathbb{Q} : q < x\}$

asked Oct 10, 2021 at 22:31

4 votes

2 answers

866 views

Prove $S_4$ has no normal subgroup of order 8, or of order 3?

asked Feb 18, 2022 at 12:36

4 votes

1 answer

85 views

If you sum all possible subsets of peoples' birthday dates in a group of 7 people, will two sets always have the same sum?

asked Oct 30, 2021 at 11:05

4 votes

1 answer

410 views

Are the positive irrational numbers closed under addition?

asked Aug 11, 2022 at 6:02

4 votes

2 answers

176 views

What is the kernel of this map $\Phi: F_2 \to \mathbb{Z}_2 \oplus \mathbb{Z}_3$?

asked Feb 21, 2022 at 3:00

4 votes

1 answer

78 views

Identify the group $(28\mathbb Z + 20\mathbb Z)/20 \mathbb Z$

asked Feb 8, 2023 at 21:13

4 votes

2 answers

116 views

What is maximum number of circles in $\mathbb R^2$ that intersect a common circle, but are otherwise disjoint?

asked Jan 18, 2023 at 4:24

4 votes

0 answers

61 views

Compute $[ \mathbb Q(\zeta_8) : \mathbb Q(i)]$ and find a basis for the extension.

asked May 4, 2023 at 6:01

3 votes

2 answers

117 views

Number of words with $3n$ letters where no $3$ consecutive letters are the same

asked Feb 10 at 14:22

3 votes

2 answers

190 views

Explicit isomorphism of algebras $\mathbb C[S_3]\cong \mathbb C \times \mathbb C \times M_2(\mathbb C)$

asked Feb 24 at 13:49

3 votes

4 answers

113 views

Number of binary strings of length $56$ vs number of permutations of English alphabet

asked Mar 2 at 20:20

3 votes

1 answer

38 views

First usage of "intersection graph" in a publication?

asked Mar 22, 2023 at 2:09

3 votes

0 answers

102 views

What is the minimum number of facets needed to fit a convex polytope between two concentric spheres?

asked Mar 22, 2023 at 22:25

3 votes

1 answer

128 views

Is the number of maximal cliques of a planar graph bounded by its number of faces?

asked Jan 16, 2023 at 12:27

3 votes

1 answer

175 views

Example of a metric space with unbounded doubling dimension

asked Nov 5, 2022 at 10:03

3 votes

1 answer

83 views

Maximal cliques on graphs on the vertices of regular $2n$-gons

asked Feb 3, 2023 at 22:51

3 votes

1 answer

73 views

Show that $G$ is a subgroup of $\operatorname{GL}_3(\mathbb R)$ and $G \cong \mathbb R^2 \rtimes (\mathbb R^\times \times \mathbb R^\times)$

asked Feb 23, 2023 at 20:56

3 votes

1 answer

301 views

Draw a cover of $S^1 \vee S^1$ whose $\pi_1$ is isomorphic to $\langle a^2,b^3,aba^{-1}b^{-1} \rangle \leq F_2$

asked Feb 22, 2022 at 13:27

3 votes

1 answer

180 views

Can the direct product of nontrivial groups $A\times B$ ever be isomorphic to a free group?

asked Mar 19, 2022 at 3:46

3 votes

0 answers

57 views

Prove that $X$ is not homotopic to any graph if its covering space is homotopic to a product space

asked Mar 31, 2022 at 14:32

3 votes

2 answers

219 views

Counting the units in a quotient ring of a polynomial ring over a field?

asked Oct 29, 2021 at 6:27

3 votes

3 answers

327 views

Continuous Bijection which is Not a Homeomorphism

asked Oct 9, 2021 at 10:42

2 votes

1 answer

86 views

Find a bijection $g:\mathbb{R} \longrightarrow \mathbb{R}\setminus \{0\}$

asked May 2, 2021 at 23:43

2 votes

0 answers

69 views

Use $\varepsilon$-$N$ definition of convergence to show $\lim (1+\frac{1}{n})^2 = 1$

asked Oct 10, 2021 at 23:15

Stack Exchange Network

149 Questions

How to rationalize the denominator $\frac{1}{1 + \sqrt[3]{5} - \sqrt[3]{25}}$

Prove that $\mathbb{Z} \times\Bbb Z_2$ and $\mathbb{Z}$ are not isomorphic.

Is there a such thing as a free group generated by a free group?

How to find all positive integers $n,k$ such that ${n\choose k}=m$ for a given $m$?

Why is $2$ the doubling constant of $\mathbb R$?

Are there any topological spaces containing no proper retracts? i.e. $A\subset X$ s.t. $\exists r:X\to A$ continuous w/ $r(a)=a,\forall a\in A$

Prove that for any $x \in \mathbb{R}$, $x = \sup \{q \in \mathbb{Q} : q < x\}$

Prove $S_4$ has no normal subgroup of order 8, or of order 3?

If you sum all possible subsets of peoples' birthday dates in a group of 7 people, will two sets always have the same sum?

Are the positive irrational numbers closed under addition?

What is the kernel of this map $\Phi: F_2 \to \mathbb{Z}_2 \oplus \mathbb{Z}_3$?

Identify the group $(28\mathbb Z + 20\mathbb Z)/20 \mathbb Z$

What is maximum number of circles in $\mathbb R^2$ that intersect a common circle, but are otherwise disjoint?

Compute $[ \mathbb Q(\zeta_8) : \mathbb Q(i)]$ and find a basis for the extension.

Number of words with $3n$ letters where no $3$ consecutive letters are the same

Explicit isomorphism of algebras $\mathbb C[S_3]\cong \mathbb C \times \mathbb C \times M_2(\mathbb C)$

Number of binary strings of length $56$ vs number of permutations of English alphabet

First usage of "intersection graph" in a publication?

What is the minimum number of facets needed to fit a convex polytope between two concentric spheres?

Is the number of maximal cliques of a planar graph bounded by its number of faces?

Example of a metric space with unbounded doubling dimension

Maximal cliques on graphs on the vertices of regular $2n$-gons

Show that $G$ is a subgroup of $\operatorname{GL}_3(\mathbb R)$ and $G \cong \mathbb R^2 \rtimes (\mathbb R^\times \times \mathbb R^\times)$

Draw a cover of $S^1 \vee S^1$ whose $\pi_1$ is isomorphic to $\langle a^2,b^3,aba^{-1}b^{-1} \rangle \leq F_2$

Can the direct product of nontrivial groups $A\times B$ ever be isomorphic to a free group?

Prove that $X$ is not homotopic to any graph if its covering space is homotopic to a product space

Counting the units in a quotient ring of a polynomial ring over a field?

Continuous Bijection which is Not a Homeomorphism

Find a bijection $g:\mathbb{R} \longrightarrow \mathbb{R}\setminus \{0\}$

Use $\varepsilon$-$N$ definition of convergence to show $\lim (1+\frac{1}{n})^2 = 1$