User math maniac.

8 votes

1 answer

222 views

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

measure-theory outer-measure

asked May 15, 2020 at 15:25

6 votes

1 answer

413 views

Isn't the Lebesgue measure space complete?

asked Jun 11, 2020 at 15:46

5 votes

2 answers

115 views

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

matrices group-theory group-homomorphism

asked Jan 27, 2020 at 7:51

5 votes

1 answer

165 views

What can be said about the sum of the series?

real-analysis sequences-and-series absolute-convergence

asked Aug 15, 2020 at 16:38

5 votes

3 answers

111 views

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

linear-algebra eigenvalues-eigenvectors rotations orthogonal-matrices fixed-points

asked Dec 12, 2020 at 19:02

4 votes

1 answer

89 views

Is $(A+B)$ necessarily singular?

matrices finite-fields examples-counterexamples

asked Jul 11, 2020 at 16:06

4 votes

2 answers

732 views

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

real-analysis integration uniform-convergence solution-verification sequence-of-function

asked Jan 16, 2020 at 15:06

4 votes

3 answers

282 views

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

abstract-algebra ring-theory ideals maximal-and-prime-ideals principal-ideal-domains

asked Apr 12, 2020 at 5:43

3 votes

0 answers

51 views

Prove that $\ell^p$ is complete.

functional-analysis measure-theory solution-verification complete-spaces

asked Dec 17, 2020 at 8:57

3 votes

1 answer

3k views

Eigenvalues of a real orthogonal matrix.

linear-algebra eigenvalues-eigenvectors orthogonal-matrices

asked Mar 31, 2019 at 5:00

3 votes

2 answers

183 views

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

limits

asked Apr 7, 2019 at 4:30

3 votes

1 answer

137 views

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

proof-writing analytic-number-theory integer-partitions

asked May 5, 2019 at 16:17

3 votes

2 answers

207 views

Problem in solving an inequality.

algebra-precalculus inequality proof-writing

asked Sep 4, 2019 at 6:12

3 votes

2 answers

66 views

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

abstract-algebra ring-theory proof-writing field-theory galois-theory

asked Oct 15, 2019 at 8:34

3 votes

1 answer

80 views

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

real-analysis limits

asked Dec 4, 2019 at 9:43

2 votes

1 answer

39 views

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

functional-analysis normed-spaces

asked Jan 1, 2020 at 8:20

2 votes

0 answers

43 views

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

abstract-algebra ring-theory proof-writing field-theory galois-theory

asked Oct 18, 2019 at 7:13

2 votes

0 answers

53 views

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

abstract-algebra ring-theory field-theory

asked Sep 17, 2019 at 4:24

2 votes

0 answers

515 views

An example of a field extension which is not Galois.

abstract-algebra ring-theory field-theory galois-theory

asked Oct 13, 2019 at 17:16

2 votes

0 answers

34 views

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

proof-verification field-theory galois-theory

asked Nov 23, 2019 at 8:04

2 votes

0 answers

56 views

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

group-theory finite-groups proof-explanation abelian-groups p-groups

asked Nov 28, 2019 at 7:29

2 votes

4 answers

204 views

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

algebra-precalculus exponential-function contest-math

asked Aug 27, 2019 at 6:28

2 votes

1 answer

89 views

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

ring-theory field-theory proof-explanation

asked Sep 24, 2019 at 7:48

2 votes

1 answer

64 views

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

ring-theory field-theory proof-explanation finite-fields

asked Sep 25, 2019 at 17:03

2 votes

1 answer

125 views

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

ring-theory maximal-and-prime-ideals

asked Jun 16, 2019 at 6:49

2 votes

2 answers

229 views

A question of arithmetic regarding erection cost of a structure.

algebra-precalculus arithmetic

asked Oct 20, 2018 at 19:46

2 votes

0 answers

69 views

Finding fundamental groups of two spaces. [closed]

algebraic-topology fundamental-groups

asked Nov 28, 2018 at 7:42

2 votes

2 answers

34 views

How to use closedness of $C$?

general-topology normed-spaces

asked Feb 4, 2019 at 13:06

2 votes

1 answer

45 views

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

modules algebraic-number-theory dedekind-domain

asked Mar 4, 2019 at 6:42

2 votes

2 answers

205 views

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

sequences-and-series proof-verification

asked Mar 22, 2019 at 16:46

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129 Questions

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

Isn't the Lebesgue measure space complete?

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

What can be said about the sum of the series?

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

Is $(A+B)$ necessarily singular?

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

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

Prove that $\ell^p$ is complete.

Eigenvalues of a real orthogonal matrix.

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

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

Problem in solving an inequality.

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

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

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

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

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

An example of a field extension which is not Galois.

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

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

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

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

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

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

A question of arithmetic regarding erection cost of a structure.

Finding fundamental groups of two spaces. [closed]

How to use closedness of $C$?

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

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