User Sid Caroline

153 votes

8 answers

22k views

Do most mathematicians know most topics in mathematics?

asked Jul 27, 2017 at 8:52

11 votes

2 answers

2k views

Why do first order languages have at most countably many symbols?

asked Oct 26, 2017 at 12:58

10 votes

1 answer

1k views

Why are short exact sequences important?

asked Aug 23, 2020 at 7:31

9 votes

2 answers

2k views

Good source of references for the classification of real semisimple Lie algebras

asked Feb 21, 2019 at 7:44

7 votes

1 answer

754 views

What is the cofinality of $\omega+1$?

asked Aug 26, 2017 at 21:17

7 votes

1 answer

783 views

How is complex analysis relevant to other areas of mathematics?

asked Jul 10, 2017 at 6:39

6 votes

2 answers

586 views

Spaces with finite bases are compact

asked Sep 11, 2017 at 9:57

6 votes

2 answers

2k views

A set is recursively enumerable iff it is the range of a total recursive function

asked Nov 2, 2017 at 11:36

5 votes

1 answer

501 views

Maximal compact topology iff compact sets are closed

asked Oct 9, 2017 at 22:20

5 votes

2 answers

2k views

A cocountable topology is not first countable

asked Sep 7, 2017 at 22:29

5 votes

6 answers

955 views

How to show that $\sin^2(1/n)\leq 1/n^2, \forall n\in\mathbb{N}?$

asked Aug 22, 2017 at 0:16

5 votes

1 answer

433 views

Proper subgroup of normalizer of a finite group impies nilpotent.

asked Jun 11, 2017 at 0:56

5 votes

0 answers

415 views

Group presentation of a direct product.

asked Jun 12, 2017 at 11:18

4 votes

2 answers

3k views

Prove that $S_n$ is isomorphic to a subgroup of $A_{n+2}$ [duplicate]

asked Jun 2, 2017 at 0:00

4 votes

2 answers

2k views

Why isn't the Cantor set a discrete topology?

asked Aug 24, 2017 at 20:11

4 votes

2 answers

796 views

$X$ is normal if and only if $A\subseteq U$ implies there exists $V$ such that $A\subseteq V\subseteq\overline{V}\subseteq U$

asked Sep 6, 2017 at 0:40

4 votes

1 answer

758 views

Is a loop in $X$ based at $a\in X$ homotopic to its reverse loop?

asked Oct 6, 2017 at 2:22

4 votes

2 answers

817 views

Prove that ordinals are comparable

asked Oct 24, 2017 at 4:02

4 votes

1 answer

170 views

Is the bifunctor of a monoidal category faithful?

asked Nov 24, 2019 at 1:41

3 votes

2 answers

650 views

Tensor product of direct sums = direct sum of tensor products?

asked Feb 21, 2021 at 3:26

3 votes

3 answers

455 views

Why is $\mathbb{Q}$ dense in $\mathbb{R}$?

asked Aug 30, 2017 at 9:11

3 votes

1 answer

652 views

Which ordinal is bigger, $\omega^\omega\omega$ or $\omega\omega^\omega$?

asked Aug 22, 2017 at 9:44

3 votes

1 answer

1k views

Why is $\omega+1+\omega+1 = \omega+\omega+1$?

asked Aug 15, 2017 at 2:42

3 votes

1 answer

3k views

A quotient space of a Hausdorff space need not be Hausdorff

asked Aug 16, 2017 at 9:19

2 votes

1 answer

1k views

metrics induce the same topology

asked Aug 16, 2017 at 4:53

2 votes

2 answers

933 views

How to compare ordinal numbers?

asked Aug 22, 2017 at 11:26

2 votes

2 answers

46 views

If $C$ is a closed subspace topology of $X$, and $S$ is closed in $C$

asked Aug 23, 2017 at 5:30

2 votes

2 answers

241 views

What does $\aleph_{\aleph_{\aleph_0}}$ stand for?

asked Aug 26, 2017 at 22:37

2 votes

2 answers

2k views

Connected components of a space $X$ are disjoint

asked Sep 9, 2017 at 8:53

2 votes

2 answers

113 views

How to axiomatize "the domain of a model has at most $n$ elements" in a first order language?

asked Sep 29, 2017 at 7:17

Stack Exchange Network

140 Questions

Do most mathematicians know most topics in mathematics?

Why do first order languages have at most countably many symbols?

Why are short exact sequences important?

Good source of references for the classification of real semisimple Lie algebras

What is the cofinality of $\omega+1$?

How is complex analysis relevant to other areas of mathematics?

Spaces with finite bases are compact

A set is recursively enumerable iff it is the range of a total recursive function

Maximal compact topology iff compact sets are closed

A cocountable topology is not first countable

How to show that $\sin^2(1/n)\leq 1/n^2, \forall n\in\mathbb{N}?$

Proper subgroup of normalizer of a finite group impies nilpotent.

Group presentation of a direct product.

Prove that $S_n$ is isomorphic to a subgroup of $A_{n+2}$ [duplicate]

Why isn't the Cantor set a discrete topology?

$X$ is normal if and only if $A\subseteq U$ implies there exists $V$ such that $A\subseteq V\subseteq\overline{V}\subseteq U$

Is a loop in $X$ based at $a\in X$ homotopic to its reverse loop?

Prove that ordinals are comparable

Is the bifunctor of a monoidal category faithful?

Tensor product of direct sums = direct sum of tensor products?

Why is $\mathbb{Q}$ dense in $\mathbb{R}$?

Which ordinal is bigger, $\omega^\omega\omega$ or $\omega\omega^\omega$?

Why is $\omega+1+\omega+1 = \omega+\omega+1$?

A quotient space of a Hausdorff space need not be Hausdorff

metrics induce the same topology

How to compare ordinal numbers?

If $C$ is a closed subspace topology of $X$, and $S$ is closed in $C$

What does $\aleph_{\aleph_{\aleph_0}}$ stand for?

Connected components of a space $X$ are disjoint

How to axiomatize "the domain of a model has at most $n$ elements" in a first order language?