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8 votes
1 answer
222 views

Prove that $\mu^* (F \setminus E) = 0.$

6 votes
1 answer
413 views

Isn't the Lebesgue measure space complete?

5 votes
2 answers
115 views

Find the cardinality of the image of $\varphi.$

5 votes
1 answer
165 views

What can be said about the sum of the series?

5 votes
3 answers
111 views

Prove that $T(v) = v,$ for some $v \in \Bbb R^3 \setminus \{0\}.$

4 votes
1 answer
89 views

Is $(A+B)$ necessarily singular?

4 votes
2 answers
732 views

Show that the sequence of functions $\{f_n\}$ is not uniformly convergent on $\Bbb R.$

4 votes
3 answers
282 views

Isn't $I$ a maximal ideal in $\Bbb Z_{11} [X]$?

3 votes
0 answers
51 views

Prove that $\ell^p$ is complete.

3 votes
1 answer
3k views

Eigenvalues of a real orthogonal matrix.

3 votes
2 answers
183 views

What will be $\lim\limits_{x \rightarrow 0^+} \left ( 2 \sin \left ( \frac 1 x \right ) + \sqrt x \sin \left ( \frac 1 x \right ) \right )^x$?

3 votes
1 answer
137 views

How to extend Euler's identity regarding partition on the unit disk?

3 votes
2 answers
207 views

Problem in solving an inequality.

3 votes
2 answers
66 views

Prove that $\chi_y = \prod\limits_{\sigma \in G} \left (X-\sigma(y) \right ).$

3 votes
1 answer
80 views

Is it necessarily true that $\lim\limits_{x \rightarrow \infty} f(x) = 0$?

2 votes
1 answer
39 views

What is $\|g\|_{\text {op}}$?

2 votes
0 answers
43 views

Can $L|K$ be a Galois extension if $\text {Fix}_{G}\ (L) = K$?

2 votes
0 answers
53 views

Is $\Bbb K^n$ a $\Bbb K$-algebra?

2 votes
0 answers
515 views

An example of a field extension which is not Galois.

2 votes
0 answers
34 views

How does $[M:K] = \#\ \text {Gal} \left (M|K \right)$?

2 votes
0 answers
56 views

Why does $\langle \bar a \rangle \cap \overline K = \{\bar e \}$?

2 votes
4 answers
204 views

Solve the equation $x^{x^5} = 5$ over $\Bbb R.$

2 votes
1 answer
89 views

Any finite subgroup of a multiplicative group of a field is cyclic.

2 votes
1 answer
64 views

For any prime number $p$ and $m \in \Bbb N$ there exists a field of cardinality $p^m.$

2 votes
1 answer
125 views

Prove that $u-i$ is a maximal ideal of $\frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$

2 votes
2 answers
229 views

A question of arithmetic regarding erection cost of a structure.

2 votes
0 answers
69 views

Finding fundamental groups of two spaces. [closed]

2 votes
2 answers
34 views

How to use closedness of $C$?

2 votes
1 answer
45 views

Does any fractional ideal of $R$ always contain a non-zero element of $R$? [closed]

2 votes
2 answers
205 views

How do I prove that $\prod\limits_{n=1}^{\infty} (1-x^n)$ is absolutely convergent for $0 \leq x < 1$?

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