User Nikolaj-K

100 votes

lim sup and lim inf of sequence of sets.

answered Jun 5, 2013 at 20:55

19 votes

"Immediate" Applications of Differential Geometry

answered Dec 9, 2011 at 22:01

14 votes

If $A^2 = I$ (Identity Matrix) then $A = \pm I$

answered Feb 5, 2012 at 20:57

14 votes

Accepted

Computing $\lim_{s \to 1} \Gamma \left(\frac{1-s}{2}\right) (s-1)$

answered Jan 14, 2013 at 12:44

13 votes

Solving for $x$: $1=\frac{1}{x}+\frac{1}{1+\frac{1}{x}}+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}+\cdots$

answered Jun 14, 2013 at 18:30

11 votes

Favourite proofs with a visualization

answered Feb 10, 2012 at 16:00

10 votes

Green's function

answered Jan 21, 2012 at 1:30

10 votes

Is a matrix multiplied with its transpose something special?

answered Jun 14, 2012 at 12:23

9 votes

Accepted

Rationale behind truth values

answered May 16, 2013 at 12:37

9 votes

Mathematics - The big picture

answered Aug 22, 2014 at 12:24

8 votes

Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$

answered Jul 24, 2013 at 14:19

8 votes

$ f(x)=f(x+1) $ and $ f(-1/x)=f(x)$

answered Jun 26, 2012 at 21:13

7 votes

how to show that $\int_0^\infty \sin(x^2) dx$ converges

answered Jan 15, 2013 at 20:51

6 votes

Is the matrix exponential map injective?

answered Jan 9, 2012 at 8:38

6 votes

Find $x$ and $y$ value in simple equation

answered Aug 16, 2012 at 11:26

6 votes

Does universal set exist?

answered Jun 5, 2013 at 10:00

6 votes

Give an example of a function $h:\mathbb{R}\backslash\mathbb{Q}\rightarrow\ \mathbb{Q}$

answered Oct 1, 2022 at 6:31

5 votes

Accepted

Is $g$ the unique function with this property?

answered Dec 16, 2014 at 18:05

5 votes

Closed form of the sum $\sum\limits_{n=0}^\infty \exp(-n^3)$

answered Apr 9, 2015 at 13:21

5 votes

How do we know whether certain mathematical theorems are circular?

answered Mar 19, 2014 at 10:09

5 votes

Given $\lambda$ and $A$, find $v$ such that $\lambda = v^{\intercal}Av$

answered Jul 23, 2012 at 18:07

5 votes

Accepted

Computing $\int_{|z|=1}|z-1|\cdot|dz|$.

answered Feb 13, 2012 at 9:18

5 votes

Accepted

What's the meaning of functional graph?

answered Jan 17, 2013 at 13:23

5 votes

Accepted

An hermitian operator problem

answered Jan 5, 2012 at 12:46

4 votes

What are other solutions to this differential equation, "similar" to $\sin x$ and $e^x$?

answered Nov 23, 2012 at 20:47

4 votes

Operator theory: $T^2=T$, but $T^{*}\neq T$

answered Feb 5, 2013 at 10:42

4 votes

A trigonometry equation problem

answered Jul 31, 2012 at 19:59

4 votes

If $(\cos \alpha + i \sin \alpha )^n = 1$ then $(\cos \alpha - i \sin \alpha )^n = 1$

answered Feb 24, 2014 at 19:18

4 votes

How to compute $\prod_{n=1}^\infty\left(1+\frac{1}{n!}\right)$?

answered Jan 13, 2015 at 13:39

4 votes

Accepted

Prove that there is a function $w > 0$ such that $\int_{0}^{1}w(x) dx \neq 0$ and $\frac{\int_{0}^{1}w(x)x^{2}dx}{\int_{0}^{1}w(x)dx} = \frac{1}{2}$?

answered Feb 24, 2015 at 9:14

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133 Answers

lim sup and lim inf of sequence of sets.

"Immediate" Applications of Differential Geometry

If $A^2 = I$ (Identity Matrix) then $A = \pm I$

Computing $\lim_{s \to 1} \Gamma \left(\frac{1-s}{2}\right) (s-1)$

Solving for $x$: $1=\frac{1}{x}+\frac{1}{1+\frac{1}{x}}+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}+\cdots$

Favourite proofs with a visualization

Green's function

Is a matrix multiplied with its transpose something special?

Rationale behind truth values

Mathematics - The big picture

Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$

$ f(x)=f(x+1) $ and $ f(-1/x)=f(x)$

how to show that $\int_0^\infty \sin(x^2) dx$ converges

Is the matrix exponential map injective?

Find $x$ and $y$ value in simple equation

Does universal set exist?

Give an example of a function $h:\mathbb{R}\backslash\mathbb{Q}\rightarrow\ \mathbb{Q}$

Is $g$ the unique function with this property?

Closed form of the sum $\sum\limits_{n=0}^\infty \exp(-n^3)$

How do we know whether certain mathematical theorems are circular?

Given $\lambda$ and $A$, find $v$ such that $\lambda = v^{\intercal}Av$

Computing $\int_{|z|=1}|z-1|\cdot|dz|$.

What's the meaning of functional graph?

An hermitian operator problem

What are other solutions to this differential equation, "similar" to $\sin x$ and $e^x$?

Operator theory: $T^2=T$, but $T^{*}\neq T$

A trigonometry equation problem

If $(\cos \alpha + i \sin \alpha )^n = 1$ then $(\cos \alpha - i \sin \alpha )^n = 1$

How to compute $\prod_{n=1}^\infty\left(1+\frac{1}{n!}\right)$?

Prove that there is a function $w > 0$ such that $\int_{0}^{1}w(x) dx \neq 0$ and $\frac{\int_{0}^{1}w(x)x^{2}dx}{\int_{0}^{1}w(x)dx} = \frac{1}{2}$?