Question

How to change proof by contradiction to pigeon hole principle?

score 129 · Answer 1 · 2026-04-11 08:09:32

129

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How to change proof by contradiction to pigeon hole principle?

Published on 11 Apr 2026 - 8:09

score 55 · Answer 2 · 2026-04-14 18:08:46

55

Views

Prove that $\{A_n\}_{n \in \mathbb{Z}}$ is a partition of $\mathbb{Z}$ where $A_n = \{m \in \mathbb{Z}: \exists q \ni m = n + 5q\}$

Published on 14 Apr 2026 - 18:08

score 59 · Answer 3 · 2026-04-11 00:20:36

59

Views

Alternative proof for existence of nth roots

Published on 11 Apr 2026 - 0:20

score 35 · Answer 4 · 2026-04-11 22:32:02

35

Views

Is $H/L$ isomorphic to $K^\times K^$ where $K^*=(K_{\ne0},\cdot)$ with $K$ field and $H, L$ certain subgroups of $GL(2,K)$?

Published on 11 Apr 2026 - 22:32

score 550 · Answer 5 · 2026-04-13 20:51:01

550

Views

Please explain how to find the probability that it passes through the mesh

Published on 13 Apr 2026 - 20:51

score 164 · Answer 6 · 2026-04-14 18:20:23

164

Views

Proving a set of vectors is a basis for the quotient map between two vector spaces

Published on 14 Apr 2026 - 18:20

score 79 · Answer 7 · 2026-04-12 19:52:53

79

Views

Proof of inequality solution

Published on 12 Apr 2026 - 19:52

score 419 · Answer 8 · 2026-03-25 03:18:51

419

Views

Finding an explicit isomorphism between $\mathbb R^4 / \ker \ T$ and $\mathbb R^2$

Published on 25 Mar 2026 - 3:18

score 378 · Answer 9 · 2026-04-16 13:19:21

378

Views

finite product of artinian rings is artinian

Published on 16 Apr 2026 - 13:19

score 114 · Answer 10 · 2026-04-15 10:25:43

114

Views

Deduce that the unit ball $\{ \textbf{x} \in \mathbb{R^n} : \| \textbf{x} \| \leq 1 \}$ is closed

Published on 15 Apr 2026 - 10:25

score 106 · Answer 11 · 2026-04-15 11:27:27

106

Views

Proof Checking: Elements of Noetherian Domains may be factored into irreducibles

Published on 15 Apr 2026 - 11:27

score 83 · Answer 12 · 2026-04-12 17:40:52

83

Views

[Proof]. A linear operator T is injective iff $N(T)= \{0\}$

Published on 12 Apr 2026 - 17:40

score 4.5k · Answer 13 · 2026-04-12 21:00:54

4.5k

Views

Proof that limit in a Hausdorff space is unique

Published on 12 Apr 2026 - 21:00

score 96 · Answer 14 · 2026-04-15 21:38:18

96

Views

Show that if $z^n$ + $z^{n-1}$ + ... + $z$ + 1 = 0 then $z$ $\neq$ 1 and $z^{n+1}$ =1.

Published on 15 Apr 2026 - 21:38

score 30 · Answer 15 · 2026-04-16 10:23:17

30

Views

Show that if $z$ is a complex number such that $z^5$ + 5$z^2$ + 7 = 0, then |$z$| > 1.

Published on 16 Apr 2026 - 10:23

List Question

How to change proof by contradiction to pigeon hole principle?

Prove that $\{A_n\}_{n \in \mathbb{Z}}$ is a partition of $\mathbb{Z}$ where $A_n = \{m \in \mathbb{Z}: \exists q \ni m = n + 5q\}$

Alternative proof for existence of nth roots

Is $H/L$ isomorphic to $K^\times K^$ where $K^*=(K_{\ne0},\cdot)$ with $K$ field and $H, L$ certain subgroups of $GL(2,K)$?

Please explain how to find the probability that it passes through the mesh

Proving a set of vectors is a basis for the quotient map between two vector spaces

Proof of inequality solution

Finding an explicit isomorphism between $\mathbb R^4 / \ker \ T$ and $\mathbb R^2$

finite product of artinian rings is artinian

Deduce that the unit ball $\{ \textbf{x} \in \mathbb{R^n} : \| \textbf{x} \| \leq 1 \}$ is closed

Proof Checking: Elements of Noetherian Domains may be factored into irreducibles

[Proof]. A linear operator T is injective iff $N(T)= \{0\}$

Proof that limit in a Hausdorff space is unique

Show that if $z^n$ + $z^{n-1}$ + ... + $z$ + 1 = 0 then $z$ $\neq$ 1 and $z^{n+1}$ =1.

Show that if $z$ is a complex number such that $z^5$ + 5$z^2$ + 7 = 0, then |$z$| > 1.

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