User legionwhale - Mathematics Stack Exchange

27 votes

2 answers

3k views

Why do we define the modulus of a complex number as we do?

asked Apr 11, 2021 at 2:31

9 votes

2 answers

164 views

Dominated convergence of series of powers

asked Nov 9, 2023 at 23:18

8 votes

1 answer

223 views

Are groups always isomorphic to their image under power maps?

asked Jul 1, 2022 at 17:20

6 votes

1 answer

219 views

Values of the Liouville function

asked Dec 18, 2021 at 17:31

4 votes

1 answer

162 views

Quotient of $\mathbb{R^*}$ by cyclic group product

asked Jun 28, 2021 at 1:47

4 votes

5 answers

621 views

When tackling trig identities, which side is the best to start from?

asked Feb 17, 2020 at 22:11

4 votes

1 answer

248 views

Numbers with 1000 digits which are the sum of the 1000th powers of their digits

asked Jul 29, 2021 at 17:14

4 votes

1 answer

276 views

Is there an corresponding concept of prime ideals in groups?

asked May 31, 2022 at 16:26

4 votes

0 answers

83 views

Homotopy lifting as iterated path lifting

asked Apr 10, 2023 at 22:33

4 votes

0 answers

189 views

Subsets of $\mathbb{Z}$ satisfying the factorial property

asked Jul 3, 2023 at 21:53

3 votes

1 answer

144 views

Proof verification of decomposition of abelian group into torsion and free groups

asked May 2, 2023 at 12:27

3 votes

1 answer

384 views

Modulus of characteristic function equal to 1 implies almost surely constant

asked May 16, 2023 at 14:56

3 votes

1 answer

58 views

Forcing fractional parts to be less than $\varepsilon$ simultaneously

asked Nov 2, 2023 at 0:41

3 votes

1 answer

186 views

Expected value of highest card before first ace

asked Sep 18, 2023 at 3:57

3 votes

1 answer

101 views

Natural way of inducing sequence of subgroups of $S_n$

asked Dec 1, 2023 at 0:34

3 votes

1 answer

44 views

Can an uncountable metric space have a concentrated point?

asked Jun 11, 2022 at 15:23

3 votes

1 answer

181 views

Do unique $n^{th}$ roots commute in groups?

asked Jun 19, 2022 at 23:31

3 votes

2 answers

54 views

Can we always pick an integer power of $e^{i \theta}$ such that its difference with $1$ has rational argument?

asked May 17, 2022 at 21:03

3 votes

0 answers

96 views

Is $\mathbb{Z}[ \alpha ]$ Noetherian for $\alpha \in \mathbb{C}$?

asked May 27, 2022 at 13:52

3 votes

1 answer

128 views

Verification of $(m+1)| \binom{2m}{m}$ and interpretation

asked Sep 23, 2022 at 20:01

3 votes

1 answer

108 views

Is there a way to solve this non-linear recurrence relation?

asked May 18, 2021 at 23:29

2 votes

0 answers

104 views

Alternative way to deduce combinatorial identity?

asked Dec 18, 2021 at 23:28

2 votes

0 answers

49 views

Sensible notion of closure of topological subspace under paths

asked Nov 23, 2022 at 15:18

2 votes

1 answer

70 views

Dense subset of $S^{n-1}$ with antipodal complement

asked Aug 7, 2022 at 14:02

2 votes

1 answer

54 views

Limits of abstract smooth surfaces

asked May 23, 2022 at 12:46

2 votes

1 answer

48 views

Open subschemes of open sets not contained in basic open sets

asked Oct 29, 2023 at 16:04

2 votes

1 answer

95 views

$R$-module structure of tensor product of $R$-algebras (Atiyah-Macdonald)

asked Sep 30, 2023 at 2:25

2 votes

1 answer

66 views

Sufficient conditions for super-exponential growth

asked Apr 1, 2023 at 20:09

2 votes

0 answers

43 views

Maximal divisor of pairwise differences

asked Apr 6, 2023 at 16:36

2 votes

1 answer

188 views

How to show that $\mathbb{E} [ e^{itX} ] = 1 \implies e^{itX} \equiv 1$ a.s.?

asked May 18, 2023 at 23:35

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59 Questions

Why do we define the modulus of a complex number as we do?

Dominated convergence of series of powers

Are groups always isomorphic to their image under power maps?

Values of the Liouville function

Quotient of $\mathbb{R^*}$ by cyclic group product

When tackling trig identities, which side is the best to start from?

Numbers with 1000 digits which are the sum of the 1000th powers of their digits

Is there an corresponding concept of prime ideals in groups?

Homotopy lifting as iterated path lifting

Subsets of $\mathbb{Z}$ satisfying the factorial property

Proof verification of decomposition of abelian group into torsion and free groups

Modulus of characteristic function equal to 1 implies almost surely constant

Forcing fractional parts to be less than $\varepsilon$ simultaneously

Expected value of highest card before first ace

Natural way of inducing sequence of subgroups of $S_n$

Can an uncountable metric space have a concentrated point?

Do unique $n^{th}$ roots commute in groups?

Can we always pick an integer power of $e^{i \theta}$ such that its difference with $1$ has rational argument?

Is $\mathbb{Z}[ \alpha ]$ Noetherian for $\alpha \in \mathbb{C}$?

Verification of $(m+1)| \binom{2m}{m}$ and interpretation

Is there a way to solve this non-linear recurrence relation?

Alternative way to deduce combinatorial identity?

Sensible notion of closure of topological subspace under paths

Dense subset of $S^{n-1}$ with antipodal complement

Limits of abstract smooth surfaces

Open subschemes of open sets not contained in basic open sets

$R$-module structure of tensor product of $R$-algebras (Atiyah-Macdonald)

Sufficient conditions for super-exponential growth

Maximal divisor of pairwise differences

How to show that $\mathbb{E} [ e^{itX} ] = 1 \implies e^{itX} \equiv 1$ a.s.?