Question

In proving that $\sqrt{a}$ is always irrational, $\forall a\in\left\{\Bbb R^+ : 1< a\neq b^2\right\}$... a different way.

score 81 · Answer 1 · 2026-03-26 11:00:55

81

Views

In proving that $\sqrt{a}$ is always irrational, $\forall a\in\left\{\Bbb R^+ : 1< a\neq b^2\right\}$... a different way.

Published on 26 Mar 2026 - 11:00

score 596 · Answer 2 · 2026-03-26 03:11:32

596

Views

Proving the equality of two fractions

Published on 26 Mar 2026 - 3:11

score 875 · Answer 3 · 2018-04-18 12:08:38

875

Views

How many ways are there to seat 7 people around a round table, if we regard two arrangements that differ by a rotation as the same?

Published on 18 Apr 2018 - 12:08

score 1.6k · Answer 4 · 2026-03-25 06:07:02

1.6k

Views

How many ways can you color the edges of a square with 4 colors?

Published on 25 Mar 2026 - 6:07

score 1.3k · Answer 5 · 2026-03-25 17:41:49

1.3k

Views

Let M and N be normal subgroups of a group G such that $M \cap N=\{e\}$. Prove that $mn=nm$ for all $m\in M$ and all $n\in N$.

Published on 25 Mar 2026 - 17:41

score 556 · Answer 6 · 2018-04-18 15:36:55

556

Views

Prove that if $A \subset B$ then $R[A] \subset R[B]$

Published on 18 Apr 2018 - 15:36

score 380 · Answer 7 · 2018-04-18 15:42:51

380

Views

Determine whether the system has unique solution, many solutions, or has no solution.

Published on 18 Apr 2018 - 15:42

score 34 · Answer 8 · 2026-03-25 23:42:32

34

Views

A parition induced on $A$ by $f^{-1}(Y_1),f^{-1}(Y_2),...,f^{-1}(Y_n)$

Published on 25 Mar 2026 - 23:42

score 49 · Answer 9 · 2026-03-25 11:14:46

49

Views

Prove that the function $f(\bar{z})=e^{2\pi i z}$ is well-defined and that it is a group-homomorphism

Published on 25 Mar 2026 - 11:14

score 1.6k · Answer 10 · 2026-03-28 06:16:45

1.6k

Views

A non-zero ring $R$ is a field if and only if for any non-zero ring $S$, any ring homomorphism from $R$ to $S$ is injective.

Published on 28 Mar 2026 - 6:16

score 126 · Answer 11 · 2026-03-29 16:33:55

126

Views

Improving clarity and argumentation with hard-to-describe combinatorial proof

Published on 29 Mar 2026 - 16:33

score 339 · Answer 12 · 2026-03-25 19:06:57

339

Views

In the hyperbolic plane, if three points are on the same side of line $L$ and equidistant from it, then those points are not collinear

Published on 25 Mar 2026 - 19:06

score 185 · Answer 13 · 2018-04-18 21:21:30

185

Views

Every bounded holomorphic function on $\mathbb{C}\backslash \{0\}$ must be constant

Published on 18 Apr 2018 - 21:21

score 239 · Answer 14 · 2018-04-19 01:05:43

239

Views

A combinatorial proof of Wilson's theorem [Proof Verification]

Published on 19 Apr 2018 - 1:05

score 30 · Answer 15 · 2026-03-26 11:18:38

30

Views

Confusion about the optimum of some (simple?) LP (min $x+y$ on square)

Published on 26 Mar 2026 - 11:18

List Question

In proving that $\sqrt{a}$ is always irrational, $\forall a\in\left\{\Bbb R^+ : 1< a\neq b^2\right\}$... a different way.

Proving the equality of two fractions

How many ways are there to seat 7 people around a round table, if we regard two arrangements that differ by a rotation as the same?

How many ways can you color the edges of a square with 4 colors?

Let M and N be normal subgroups of a group G such that $M \cap N=\{e\}$. Prove that $mn=nm$ for all $m\in M$ and all $n\in N$.

Prove that if $A \subset B$ then $R[A] \subset R[B]$

Determine whether the system has unique solution, many solutions, or has no solution.

A parition induced on $A$ by $f^{-1}(Y_1),f^{-1}(Y_2),...,f^{-1}(Y_n)$

Prove that the function $f(\bar{z})=e^{2\pi i z}$ is well-defined and that it is a group-homomorphism

A non-zero ring $R$ is a field if and only if for any non-zero ring $S$, any ring homomorphism from $R$ to $S$ is injective.

Improving clarity and argumentation with hard-to-describe combinatorial proof

In the hyperbolic plane, if three points are on the same side of line $L$ and equidistant from it, then those points are not collinear

Every bounded holomorphic function on $\mathbb{C}\backslash \{0\}$ must be constant

A combinatorial proof of Wilson's theorem [Proof Verification]

Confusion about the optimum of some (simple?) LP (min $x+y$ on square)

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