User José Carlos Santos - Mathematics Stack Exchange

130 votes

27 answers

13k views

Unexpected examples of natural logarithm

asked Jul 3, 2017 at 13:07

61 votes

3 answers

3k views

Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$

asked Oct 2, 2017 at 10:17

28 votes

2 answers

2k views

Is every matrix conjugate to its transpose in a continuous way?

asked Dec 14, 2018 at 10:03

25 votes

1 answer

1k views

Constructing the reals from the integers

asked Aug 25, 2017 at 14:41

20 votes

6 answers

910 views

Proving a theorem using its converse

asked Apr 15, 2020 at 15:42

19 votes

1 answer

989 views

Must a continuous, non-constant, and periodic functions have a smallest period?

asked Oct 16, 2019 at 7:58

19 votes

5 answers

1k views

An absolutely convergent series of rational numbers which does not converge to a rational number [duplicate]

asked Mar 6, 2022 at 18:46

18 votes

3 answers

585 views

Egyptian fractions with very large denominators

asked Jul 20, 2018 at 9:34

15 votes

1 answer

605 views

Is the space $\mathcal C([0,1])$ endowed with the sup norm homeomorphic to $\mathcal C([0,1])$ endowed with the integral norm?

asked Oct 17, 2021 at 14:36

12 votes

1 answer

546 views

Why those who dislike the fact that the reals are uncountable always attack Cantor's diagonal proof?

asked Aug 19, 2017 at 14:50

11 votes

1 answer

296 views

On prime numbers of the form $7\times10^n+69$ and the lights out puzzle

asked Nov 2, 2017 at 15:27

11 votes

1 answer

673 views

Must a continuous and periodic functions have a smallest period?

asked Oct 11, 2018 at 10:28

10 votes

1 answer

278 views

A rearrangement of a conditionally convergent series is seldom convergent

asked Apr 14, 2022 at 17:38

10 votes

1 answer

304 views

A continuous function from $\Bbb Q$ into $\Bbb Q$ which is never a rational function

asked Feb 14, 2021 at 9:09

9 votes

1 answer

287 views

Geometrical constructions using conics

asked Mar 20, 2018 at 11:06

7 votes

0 answers

410 views

Must a differentiable function $f$ be constant if $f'$ is always $0$ and the domain is connected?

asked Mar 10, 2021 at 14:59

6 votes

2 answers

253 views

Computing sum of lengths of legs of a right triangle

asked Feb 4, 2019 at 9:36

5 votes

2 answers

834 views

A series whose convergence is equivalent to the Riemann hypothesis

asked Jan 21, 2019 at 14:13

5 votes

4 answers

676 views

Speeding up the convergence of $\zeta(2)$

asked Jun 22, 2017 at 9:27

5 votes

4 answers

811 views

Lines tangent to a parabola

asked Jan 19, 2020 at 17:57

4 votes

2 answers

502 views

On determinants and common divisors

asked Dec 9, 2017 at 9:44

4 votes

2 answers

475 views

Are there always matrices $X$ and $Y$ such that $XY=A$ and $YX=B$?

asked Jun 27, 2018 at 15:40

3 votes

2 answers

5k views

A criterion for Riemann integrability

asked Nov 9, 2017 at 9:52

2 votes

1 answer

660 views

On switches and light bulbs

asked May 26, 2017 at 16:45

2 votes

1 answer

439 views

Tiling a board with domino pieces

asked Nov 2, 2018 at 11:52

2 votes

1 answer

288 views

Constructing a circle passing through a complex number $z$, its square roots, and $1$

asked Sep 26, 2022 at 9:52

2 votes

1 answer

659 views

An example of a non-paracompact topological space

asked Nov 21, 2021 at 15:38

1 vote

1 answer

562 views

Non-repeating decimal expansion of known number

asked Jun 26, 2017 at 16:06

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28 Questions

Unexpected examples of natural logarithm

Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$

Is every matrix conjugate to its transpose in a continuous way?

Constructing the reals from the integers

Proving a theorem using its converse

Must a continuous, non-constant, and periodic functions have a smallest period?

An absolutely convergent series of rational numbers which does not converge to a rational number [duplicate]

Egyptian fractions with very large denominators

Is the space $\mathcal C([0,1])$ endowed with the sup norm homeomorphic to $\mathcal C([0,1])$ endowed with the integral norm?

Why those who dislike the fact that the reals are uncountable always attack Cantor's diagonal proof?

On prime numbers of the form $7\times10^n+69$ and the lights out puzzle

Must a continuous and periodic functions have a smallest period?

A rearrangement of a conditionally convergent series is seldom convergent

A continuous function from $\Bbb Q$ into $\Bbb Q$ which is never a rational function

Geometrical constructions using conics

Must a differentiable function $f$ be constant if $f'$ is always $0$ and the domain is connected?

Computing sum of lengths of legs of a right triangle

A series whose convergence is equivalent to the Riemann hypothesis

Speeding up the convergence of $\zeta(2)$

Lines tangent to a parabola

On determinants and common divisors

Are there always matrices $X$ and $Y$ such that $XY=A$ and $YX=B$?

A criterion for Riemann integrability

On switches and light bulbs

Tiling a board with domino pieces

Constructing a circle passing through a complex number $z$, its square roots, and $1$

An example of a non-paracompact topological space

Non-repeating decimal expansion of known number