User ZFR

21 votes

3 answers

1k views

Sum of series $\sum \limits_{k=1}^{\infty}\frac{\sin^3 3^k}{3^k}$

sequences-and-series

asked Jan 23, 2017 at 7:00

18 votes

2 answers

9k views

Infinite group has infinitely many subgroups, namely cyclic subgroups.

asked Nov 30, 2017 at 16:04

16 votes

3 answers

2k views

Erroneous proof that derivative of function is always continuous

real-analysis fake-proofs

asked Apr 15, 2021 at 1:49

15 votes

5 answers

3k views

Number which is simultaneously sum of 2 and 3 squares [closed]

number-theory

asked Nov 25, 2017 at 19:12

15 votes

2 answers

5k views

Every separable metric space has a countable base

general-topology metric-spaces solution-verification separable-spaces second-countable

asked Jun 3, 2016 at 4:59

15 votes

7 answers

24k views

A finite set is closed

real-analysis metric-spaces

asked Jun 8, 2015 at 21:50

10 votes

2 answers

10k views

Ternary representation of Cantor set

real-analysis cantor-set

asked Aug 30, 2015 at 18:56

10 votes

2 answers

2k views

Solving $x^2+\frac{81x^2}{(9+x)^2}=40$ [duplicate]

algebra-precalculus

asked Apr 19, 2016 at 10:54

9 votes

3 answers

7k views

Bounded and closed but not compact in rational numbers

real-analysis general-topology

asked Jul 9, 2015 at 20:11

9 votes

2 answers

3k views

The equivalence of definitions Riemann integral

real-analysis riemann-integration

asked Dec 31, 2015 at 9:04

8 votes

3 answers

2k views

Monotone Convergence theorem for decreasing sequence

real-analysis measure-theory proof-verification monotone-functions

asked Jun 13, 2016 at 18:35

8 votes

1 answer

1k views

Definition of isomorphism from Herstein's book

abstract-algebra group-theory definition

asked Dec 23, 2017 at 16:09

8 votes

2 answers

516 views

Problem 30 from Shakarchi Stein's book

real-analysis measure-theory

asked Sep 28, 2018 at 23:04

7 votes

2 answers

687 views

Difference between topologically complete space and complete metric space

general-topology metric-spaces

asked Nov 3, 2019 at 1:36

7 votes

3 answers

486 views

Theorem 4.22 from baby Rudin

real-analysis

asked Sep 12, 2015 at 16:13

6 votes

1 answer

1k views

Discontinuity of Dirichlet function

real-analysis proof-verification

asked Sep 13, 2015 at 9:36

6 votes

2 answers

1k views

Every open set in the real line is the countable union of disjoint intervals

real-analysis general-topology

asked Aug 10, 2015 at 4:34

6 votes

1 answer

630 views

Dirichlet series

real-analysis sequences-and-series convergence-divergence

asked May 13, 2014 at 18:48

6 votes

1 answer

131 views

Compact set of real numbers with countably many limit points.

real-analysis general-topology compactness

asked Jul 7, 2015 at 20:10

6 votes

2 answers

256 views

Proof $\int \limits_{0}^{\infty}\left(\frac{\sin x}{x}\right)^2dx=\frac{\pi}{2}$ by definition

real-analysis

asked Jan 15, 2016 at 11:16

6 votes

2 answers

2k views

Definition of positive measure

real-analysis measure-theory

asked May 22, 2016 at 6:07

6 votes

3 answers

130 views

Solve the equation $\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}$

algebra-precalculus

asked Apr 14, 2016 at 7:28

6 votes

1 answer

217 views

$\int \limits_{E}|f|d\mu<\varepsilon$ whenever $\mu(E)<\delta$.

real-analysis measure-theory proof-verification

asked Jun 13, 2016 at 17:38

6 votes

3 answers

686 views

Theorem 2.17 from RCA Rudin

real-analysis general-topology measure-theory

asked Jun 25, 2016 at 5:32

6 votes

1 answer

224 views

Theorem 2.22 from RCA Rudin

real-analysis measure-theory

asked Jul 2, 2016 at 7:05

6 votes

2 answers

759 views

Problem 15 from Herstein's book

functions elementary-set-theory

asked Nov 8, 2017 at 17:21

6 votes

2 answers

297 views

Pigeonhole principle in finite sequence

combinatorics algebra-precalculus pigeonhole-principle

asked Dec 20, 2017 at 16:03

6 votes

2 answers

102 views

Evaluate $\sum\limits_{n=1}^{2016}\frac{1}{n!+(n+1)!+(n+2)!}$

sequences-and-series

asked Jan 22, 2018 at 7:55

6 votes

3 answers

211 views

Coloring of $\mathbb{R}^3$ into 3 colors

combinatorics proof-verification contest-math

asked Nov 17, 2017 at 20:55

6 votes

2 answers

436 views

A convergent sequence has either a maximum or a minimum or both.

real-analysis sequences-and-series

asked Aug 3, 2021 at 14:53

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753 Questions

Sum of series $\sum \limits_{k=1}^{\infty}\frac{\sin^3 3^k}{3^k}$

Infinite group has infinitely many subgroups, namely cyclic subgroups.

Erroneous proof that derivative of function is always continuous

Number which is simultaneously sum of 2 and 3 squares [closed]

Every separable metric space has a countable base

A finite set is closed

Ternary representation of Cantor set

Solving $x^2+\frac{81x^2}{(9+x)^2}=40$ [duplicate]

Bounded and closed but not compact in rational numbers

The equivalence of definitions Riemann integral

Monotone Convergence theorem for decreasing sequence

Definition of isomorphism from Herstein's book

Problem 30 from Shakarchi Stein's book

Difference between topologically complete space and complete metric space

Theorem 4.22 from baby Rudin

Discontinuity of Dirichlet function

Every open set in the real line is the countable union of disjoint intervals

Dirichlet series

Compact set of real numbers with countably many limit points.

Proof $\int \limits_{0}^{\infty}\left(\frac{\sin x}{x}\right)^2dx=\frac{\pi}{2}$ by definition

Definition of positive measure

Solve the equation $\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}$

$\int \limits_{E}|f|d\mu<\varepsilon$ whenever $\mu(E)<\delta$.

Theorem 2.17 from RCA Rudin

Theorem 2.22 from RCA Rudin

Problem 15 from Herstein's book

Pigeonhole principle in finite sequence

Evaluate $\sum\limits_{n=1}^{2016}\frac{1}{n!+(n+1)!+(n+2)!}$

Coloring of $\mathbb{R}^3$ into 3 colors

A convergent sequence has either a maximum or a minimum or both.