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user121418
  • Member for 8 years, 7 months
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9 votes
3 answers
1k views

For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$

8 votes
1 answer
150 views

Find $\lim_{n\to\infty}\int_{-\pi}^{\pi}f(t)\cos^2(nt) \,dt$

7 votes
1 answer
826 views

Does there exist any continuous but not uniformly continuous function $f(x)$ such that $\sin(f(x))$ is uniformly continuous?

6 votes
3 answers
5k views

If $N$ is a normal subgroup of a group $G$, and $M$ is a characteristic subgroup of $N$, then $M$ is a normal subgroup of G.

6 votes
3 answers
164 views

Can the following integral be computed?

4 votes
3 answers
579 views

Find the largest interval for which the following series is convergent at all points x in it

3 votes
1 answer
1k views

The distance function on a metric space

2 votes
1 answer
734 views

Is the set of all matrices in M(n;R) all of whose eigenvalues satisfy the condition |λ|≤2. compact?

1 vote
2 answers
314 views

If $\sum n^2 a_n^2<\infty$ then $\sum a_n$ is convergent. [duplicate]

1 vote
2 answers
245 views

Let $f:(0,1)→R$ be continuous. Pick out the statements which imply that $f$ is uniformly continuous.

1 vote
3 answers
315 views

Fixed point and period of continuous function

1 vote
1 answer
125 views

Is there any relation between Minimal polynomial of a matrix in M(n,C) and its diagonalizablity?

1 vote
2 answers
155 views

trouble calculating sum of the series $ \sum\left(\frac{n^2}{2^n}\right) $

1 vote
1 answer
123 views

eigen value problem of the following matrix [duplicate]

1 vote
1 answer
947 views

Which of the following form an ideal in this ring?

-1 votes
1 answer
57 views

$\lim_{n\to\infty}((\sum_{r=1}^{k}(n+r)^m/n^{m-1})-kn)$ where $m,k > 0$ are fixed integers