User Nicol

34 votes

9 answers

18k views

Are there rigorous formulation and proof of the pigeonhole principle?

asked Dec 28, 2014 at 16:07

32 votes

11 answers

44k views

Proving that $\arctan(x)+\arctan(1/x)=\pm \pi/2$, could this line of reasoning possibly be correct?

asked Sep 11, 2015 at 5:59

9 votes

0 answers

290 views

Olympic number theory problem: is this solution fine and sufficiently well written?

asked Jan 31, 2015 at 17:56

5 votes

3 answers

3k views

Proof that an infinite subset of $\mathbb{N}$ is countable [duplicate]

asked Apr 18, 2015 at 14:13

4 votes

1 answer

258 views

The set of algebraic numbers is countable: is this proof correct and well written?

asked Jun 2, 2015 at 16:46

4 votes

2 answers

489 views

Is this proof correct? Prove that a continuous, periodic and non-constant function has a smallest period

asked Nov 8, 2016 at 20:28

3 votes

1 answer

941 views

Is this proof of Taylor's theorem correct and mathematically well written?

asked Sep 24, 2016 at 17:19

3 votes

2 answers

102 views

Showing that $e^{\frac{x}{a}}\simeq \sqrt{\frac{a+x}{a-x}}$

asked Sep 30, 2016 at 11:12

3 votes

2 answers

2k views

Does every subset of a metric space have an open cover?

asked Mar 26, 2015 at 17:32

3 votes

0 answers

127 views

Is this proof of a mathematical olympiad problem correct?

asked Jan 19, 2015 at 18:15

3 votes

4 answers

183 views

How to calculate $\lim_{x\to0}\frac{1}{x}\left(\sqrt[3]{\frac{1-\sqrt{1-x}}{\sqrt{1+x}-1}}-1\right)$

asked Sep 1, 2015 at 18:42

3 votes

0 answers

73 views

Exercise on limits: is this proof correct?

asked Sep 7, 2015 at 20:40

3 votes

1 answer

129 views

Is it incorrect to write $\int f(g(x))g'(x)dx=\int f(t) dt$?

asked Feb 22, 2016 at 18:06

3 votes

1 answer

103 views

Why were affine spaces defined so?

asked Sep 11, 2014 at 23:45

2 votes

3 answers

3k views

Prove that if $\sum |a_n|^2$ converges then $ \sum \frac{a_n}{n}$ converges [duplicate]

asked Sep 1, 2016 at 17:47

2 votes

2 answers

387 views

Does probability depend on knowledge?

asked Feb 16, 2016 at 11:05

2 votes

0 answers

781 views

If $f$ is continuous and injective on an interval, then it is strictly monotonic- what's wrong with this proof?

asked Sep 10, 2015 at 23:25

2 votes

1 answer

61 views

Is the solution of this trivial group theory exercise correct?

asked Dec 27, 2014 at 16:00

2 votes

1 answer

468 views

Exercise from (Baby) Rudin (Chapter 3, exercise 13): is this proof correct? Is it well-written?

asked Aug 30, 2015 at 22:01

2 votes

0 answers

62 views

Limits- when is this substitution allowed?

asked Oct 18, 2015 at 19:31

2 votes

3 answers

122 views

How can this sum be maximized?

asked Nov 16, 2015 at 15:19

1 vote

3 answers

201 views

How do you calculate this limit without using L'Hopital or Taylor?

asked Dec 8, 2015 at 9:33

1 vote

0 answers

164 views

Counterexamples in integral calculus: do functions like these exist?

asked Jan 31, 2016 at 16:57

1 vote

0 answers

101 views

Proving the continuity of the function $f(x)=x^\alpha$ through power series

asked Sep 4, 2015 at 12:26

1 vote

1 answer

57 views

Why does $\frac{\frac12 x+\frac18x^2+O(x^3)}{\frac12x-\frac18x^2+O(x^3)}=1+\frac12x+O(x^2)$?

asked Apr 24, 2016 at 18:00

1 vote

0 answers

25 views

If a differentiable function is defined on a closed interval, can I expand it with Taylor formula about the extrema?

asked Sep 22, 2016 at 13:48

1 vote

3 answers

104 views

If $a\in A$ and $A\in B$, is $a\in B$? [duplicate]

asked Jan 14, 2015 at 16:56

1 vote

0 answers

512 views

There exist a bijection between the Real numbers and points of a straight

asked Aug 22, 2014 at 22:54

1 vote

1 answer

64 views

Elementary combinatorics problem: which answer is the right one?

asked Nov 22, 2014 at 22:48

1 vote

3 answers

289 views

Olympic elementary combinatorics problem

asked Nov 25, 2014 at 16:17

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50 Questions

Are there rigorous formulation and proof of the pigeonhole principle?

Proving that $\arctan(x)+\arctan(1/x)=\pm \pi/2$, could this line of reasoning possibly be correct?

Olympic number theory problem: is this solution fine and sufficiently well written?

Proof that an infinite subset of $\mathbb{N}$ is countable [duplicate]

The set of algebraic numbers is countable: is this proof correct and well written?

Is this proof correct? Prove that a continuous, periodic and non-constant function has a smallest period

Is this proof of Taylor's theorem correct and mathematically well written?

Showing that $e^{\frac{x}{a}}\simeq \sqrt{\frac{a+x}{a-x}}$

Does every subset of a metric space have an open cover?

Is this proof of a mathematical olympiad problem correct?

How to calculate $\lim_{x\to0}\frac{1}{x}\left(\sqrt[3]{\frac{1-\sqrt{1-x}}{\sqrt{1+x}-1}}-1\right)$

Exercise on limits: is this proof correct?

Is it incorrect to write $\int f(g(x))g'(x)dx=\int f(t) dt$?

Why were affine spaces defined so?

Prove that if $\sum |a_n|^2$ converges then $ \sum \frac{a_n}{n}$ converges [duplicate]

Does probability depend on knowledge?

If $f$ is continuous and injective on an interval, then it is strictly monotonic- what's wrong with this proof?

Is the solution of this trivial group theory exercise correct?

Exercise from (Baby) Rudin (Chapter 3, exercise 13): is this proof correct? Is it well-written?

Limits- when is this substitution allowed?

How can this sum be maximized?

How do you calculate this limit without using L'Hopital or Taylor?

Counterexamples in integral calculus: do functions like these exist?

Proving the continuity of the function $f(x)=x^\alpha$ through power series

Why does $\frac{\frac12 x+\frac18x^2+O(x^3)}{\frac12x-\frac18x^2+O(x^3)}=1+\frac12x+O(x^2)$?

If a differentiable function is defined on a closed interval, can I expand it with Taylor formula about the extrema?

If $a\in A$ and $A\in B$, is $a\in B$? [duplicate]

There exist a bijection between the Real numbers and points of a straight

Elementary combinatorics problem: which answer is the right one?

Olympic elementary combinatorics problem