User k.stm

141 votes

Accepted

Proof of triangle inequality

answered Feb 18, 2013 at 19:12

44 votes

Accepted

Meaning of the backslash operator on sets

answered Dec 25, 2014 at 23:26

26 votes

How to prove the continuity of the metric function?

answered Jan 26, 2013 at 14:02

22 votes

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If Gal(K,Q) is abelian then |Gal(K,Q)|=n

answered Feb 8, 2014 at 13:10

20 votes

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Example of a non-splitting exact sequence $0 → M → M\oplus N → N → 0$

answered Dec 27, 2014 at 11:26

17 votes

Is every element in a set also an element of the powerset?

answered Jun 21, 2013 at 11:34

15 votes

Accepted

What is the rule for something divided by itself equaling 1?

answered May 5, 2016 at 22:31

15 votes

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$K$ is a splitting field $\iff$ any irreducible polynomial with a root in $K$ splits completely over $K$.

answered Aug 2, 2017 at 20:00

13 votes

Method of finding a p-adic expansion to a rational number

answered Mar 12, 2015 at 16:03

11 votes

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Prove that G\S generates G

answered Mar 31, 2015 at 7:43

11 votes

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From any ten naturals, find some numbers whose sum is divisible by $ 10.$

answered Mar 31, 2015 at 8:20

11 votes

Is product of two closed sets closed?

answered Aug 30, 2013 at 8:10

11 votes

How to show $\mathbf{Q} $ is not free

answered Dec 19, 2014 at 17:15

11 votes

Why is “or” (in logic) sometimes equivalent to “and” (in natural language)?

answered Jul 15, 2017 at 11:15

9 votes

Accepted

$f^2$ and $f^3$ are holomorphic implies $f$ is holomorphic.

answered May 6, 2014 at 13:02

9 votes

Solve $\dfrac{1}{1+\frac{1}{1+\ddots}}$

answered May 1, 2013 at 12:36

9 votes

Show that $f$ cannot have infinitely many zeroes in $[0, 1]$.

answered Mar 17, 2013 at 12:18

9 votes

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Category of sets, $\mathrm{I}_{\emptyset}$

answered Nov 13, 2019 at 23:09

9 votes

Is an automorphism a function or a group?

answered Jul 22, 2020 at 20:26

9 votes

Understanding $\mathbb{C} \otimes_{\mathbb{Q}} \mathbb{C}$

answered Jul 27, 2019 at 21:14

8 votes

Accepted

Relation between the notions connected and disconnect, confused

answered Jan 22, 2013 at 21:00

8 votes

Representing $\mathbb{R}/\mathbb{Z}$ as a matrix group.

answered Jul 16, 2013 at 18:16

8 votes

Creating surjective holomorphic map from unit disc to $\mathbb{C}$?

answered Nov 24, 2014 at 9:04

8 votes

Ring whose all ideals are double-sided is commutative?

answered Dec 13, 2014 at 10:57

8 votes

Is any subring of a Euclidean domain a unique factorization domain?

answered Dec 25, 2013 at 9:02

8 votes

Accepted

an example of an interesting connected topological space

answered Apr 2, 2014 at 7:57

8 votes

If two continuous maps into a Hausdorff space agree on a dense subset, they are identically equal

answered Dec 28, 2014 at 23:50

8 votes

Accepted

Let $G$ be a group and $A\subseteq G$. Showing $\{g\in G: gag^{-1}\in A \text{ for all } a\in A\}$ does not have to be a subgroup of $G$.

answered Aug 23, 2019 at 20:14

8 votes

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Every group is solvable, fake proof.

answered Jan 31, 2018 at 10:27

8 votes

Accepted

How come the $\epsilon-\delta$ definition of continuity is preferred over the sequential definition of continuity?

answered Jun 8, 2019 at 0:30

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396 Answers

Proof of triangle inequality

Meaning of the backslash operator on sets

How to prove the continuity of the metric function?

If Gal(K,Q) is abelian then |Gal(K,Q)|=n

Example of a non-splitting exact sequence $0 → M → M\oplus N → N → 0$

Is every element in a set also an element of the powerset?

What is the rule for something divided by itself equaling 1?

$K$ is a splitting field $\iff$ any irreducible polynomial with a root in $K$ splits completely over $K$.

Method of finding a p-adic expansion to a rational number

Prove that G\S generates G

From any ten naturals, find some numbers whose sum is divisible by $ 10.$

Is product of two closed sets closed?

How to show $\mathbf{Q} $ is not free

Why is “or” (in logic) sometimes equivalent to “and” (in natural language)?

$f^2$ and $f^3$ are holomorphic implies $f$ is holomorphic.

Solve $\dfrac{1}{1+\frac{1}{1+\ddots}}$

Show that $f$ cannot have infinitely many zeroes in $[0, 1]$.

Category of sets, $\mathrm{I}_{\emptyset}$

Is an automorphism a function or a group?

Understanding $\mathbb{C} \otimes_{\mathbb{Q}} \mathbb{C}$

Relation between the notions connected and disconnect, confused

Representing $\mathbb{R}/\mathbb{Z}$ as a matrix group.

Creating surjective holomorphic map from unit disc to $\mathbb{C}$?

Ring whose all ideals are double-sided is commutative?

Is any subring of a Euclidean domain a unique factorization domain?

an example of an interesting connected topological space

If two continuous maps into a Hausdorff space agree on a dense subset, they are identically equal

Let $G$ be a group and $A\subseteq G$. Showing $\{g\in G: gag^{-1}\in A \text{ for all } a\in A\}$ does not have to be a subgroup of $G$.

Every group is solvable, fake proof.

How come the $\epsilon-\delta$ definition of continuity is preferred over the sequential definition of continuity?