JKnecht's user avatar
JKnecht's user avatar
JKnecht's user avatar
JKnecht
  • Member for 8 years, 2 months
  • Last seen more than 2 years ago
  • Sweden
15 votes
3 answers
2k views

Use this sequence to prove that there are infinitely many prime numbers. [duplicate]

13 votes
6 answers
3k views

How to prove that $ {\mathbf{GL}_{n}}(\mathbb{R}) $ is dense in $ {\mathbf{M}_{n}}(\mathbb{R}) $

6 votes
1 answer
674 views

Looking for good books about simulating stochastic processes.

5 votes
2 answers
197 views

Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$

5 votes
0 answers
2k views

$X$ and $Y$ are homeomorphic. Show that also their one-point compactifications are homeomorphic.

5 votes
2 answers
756 views

Infinitely uncountable set with only isolated points.

5 votes
1 answer
307 views

How many base $10$ numbers are there with $n$ digits and an even number of zeros?

4 votes
4 answers
328 views

Prove: $\sin x \ln \left(\frac{1 + \sin x}{1 - \sin x}\right) \geq 2x^2$

3 votes
2 answers
2k views

Specific example of a space that is separable but not second countable.

3 votes
2 answers
156 views

Show that the integer nearest to $\frac{n!}{e}$ $(n \geq 2)$ is divisible by $n − 1$ but not by $n$.

3 votes
3 answers
3k views

Random Walk on a Cube

3 votes
0 answers
276 views

Random process involving CDF and PDF of standard normal.

3 votes
1 answer
787 views

Find a homeomorphism of the sphere with itself

2 votes
1 answer
713 views

$M/M/2/4$ simulation of the probability that the queue gets full during first $10$ time units.

2 votes
1 answer
2k views

Find a random process that is wide-sense stationary (WSS) but not strict-sense stationary etc.

2 votes
2 answers
97 views

Evaluate $\int_{-\pi}^{\pi}\frac {\sin nx}{(1+2^x) \sin x} $

2 votes
2 answers
333 views

Show that there is an open set $U$ in the topological group $G$ such that $1 \in U$ and $xU \cap UH = ∅$, where $H$ is a closed subgroup.

2 votes
1 answer
670 views

Show that a function defined on a subset of a metric space is well-defined and continuous.

2 votes
1 answer
7k views

Find expected time to reach a state in a Markov chain

2 votes
1 answer
254 views

Dense on the unit circle

2 votes
1 answer
273 views

Show that if $H$ is a normal subgroup of $G$ then so is $\bar{H}$.

2 votes
2 answers
125 views

Proof of $\aleph_0^{\aleph_0} = \mathbb{c}$ without using Cantor's $2^{\aleph_0} = \mathbb{c}$

2 votes
1 answer
65 views

Regarding part of proof of proposition: Any topological group $(G, \tau)$ which is a $T_1$-space is also a Hausdorff space.

2 votes
1 answer
78 views

A subspace of a mapping space?

2 votes
1 answer
234 views

Show that $X$ is Hausdorff.

2 votes
1 answer
243 views

$(0,1)^n$ a normal space but $(0,1)^{\mathbb{R}}$ not normal?

2 votes
2 answers
141 views

Prove that $A_n = C_n$, the $n$th Catalan number.

2 votes
2 answers
4k views

How many ordered subsets of a set?

2 votes
0 answers
99 views

Prove that any proper map $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$ is unbounded.

2 votes
1 answer
181 views

Find homeomorphic and non-homeomorphic pairs among the spaces $A, B$ and $C$.