Question

Please critique my proof that $\sqrt{12}$ is irrational

score 997 · Answer 1 · 2026-04-12 11:32:06

997

Views

Please critique my proof that $\sqrt{12}$ is irrational

Published on 12 Apr 2026 - 11:32

score 199 · Answer 2 · 2026-04-12 08:11:17

199

Views

Spivak's Calculus on Manifolds - Problem 1-30.

Published on 12 Apr 2026 - 8:11

score 197 · Answer 3 · 2026-04-14 08:49:10

197

Views

Exercise 12.5 from Humphreys

Published on 14 Apr 2026 - 8:49

score 64k · Answer 4 · 2026-04-14 21:56:46

64k

Views

Prove that the square root of a positive integer is either an integer or irrational

Published on 14 Apr 2026 - 21:56

score 1.1k · Answer 5 · 2026-04-12 07:47:58

1.1k

Views

Identify the Quotient Group $G/H$ Using the First Isomorphism Theorem

Published on 12 Apr 2026 - 7:47

score 92 · Answer 6 · 2026-04-17 04:49:03

92

Views

Given $7$ marbles in a box, $3$ are white and numbered from $1$ to $3$ and other $4$ are grey and numbered from $4$ to $7$. Calculate Probabilities

Published on 17 Apr 2026 - 4:49

score 88 · Answer 7 · 2026-04-17 14:49:42

88

Views

For $S=\sqrt{2000^2-1^2}+\sqrt{2000^2-2^2}+\sqrt{2000^2-3^2}+\ldots+\sqrt{2000^2-2000^2}$, find $\frac{2}{2000^2}\times(2000+2S)$.

Published on 17 Apr 2026 - 14:49

score 2.9k · Answer 8 · 2026-04-16 10:10:09

2.9k

Views

Define the relation $\mathscr{R}$ on $\Bbb Z$ by $x \mathscr{R} y$ iff $xy >0$. I wish to examine several properties of this relation.

Published on 16 Apr 2026 - 10:10

score 15.1k · Answer 9 · 2026-04-10 08:42:38

15.1k

Views

Proof for infinity matrix norm

Published on 10 Apr 2026 - 8:42

score 15.8k · Answer 10 · 2026-04-12 07:49:24

15.8k

Views

A normal subgroup is the union of conjugacy classes.

Published on 12 Apr 2026 - 7:49

score 31.4k · Answer 11 · 2026-04-15 22:32:23

31.4k

Views

Prove that $a * b = a + b - ab$ defines a group operation on $\Bbb R \setminus \{1\}$

Published on 15 Apr 2026 - 22:32

score 5.6k · Answer 12 · 2026-04-16 07:22:15

5.6k

Views

If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$

Published on 16 Apr 2026 - 7:22

score 303 · Answer 13 · 2026-04-18 11:43:37

303

Views

Prove by induction that $\sum_{r=0}^{n}\binom nr =2^k$

Published on 18 Apr 2026 - 11:43

score 135 · Answer 14 · 2026-04-19 12:03:45

135

Views

Did i solved the equation correctly?

Published on 19 Apr 2026 - 12:03

score 1.5k · Answer 15 · 2026-04-15 22:22:31

1.5k

Views

If $C \subset B$ where $B$ is a bounded subset of a metric space $(X, d)$, then $C$ is bbd and $\operatorname{diam} C \leq \operatorname{diam} B$

Published on 15 Apr 2026 - 22:22

List Question

Please critique my proof that $\sqrt{12}$ is irrational

Spivak's Calculus on Manifolds - Problem 1-30.

Exercise 12.5 from Humphreys

Prove that the square root of a positive integer is either an integer or irrational

Identify the Quotient Group $G/H$ Using the First Isomorphism Theorem

Given $7$ marbles in a box, $3$ are white and numbered from $1$ to $3$ and other $4$ are grey and numbered from $4$ to $7$. Calculate Probabilities

For $S=\sqrt{2000^2-1^2}+\sqrt{2000^2-2^2}+\sqrt{2000^2-3^2}+\ldots+\sqrt{2000^2-2000^2}$, find $\frac{2}{2000^2}\times(2000+2S)$.

Define the relation $\mathscr{R}$ on $\Bbb Z$ by $x \mathscr{R} y$ iff $xy >0$. I wish to examine several properties of this relation.

Proof for infinity matrix norm

A normal subgroup is the union of conjugacy classes.

Prove that $a * b = a + b - ab$ defines a group operation on $\Bbb R \setminus \{1\}$

If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$

Prove by induction that $\sum_{r=0}^{n}\binom nr =2^k$

Did i solved the equation correctly?

If $C \subset B$ where $B$ is a bounded subset of a metric space $(X, d)$, then $C$ is bbd and $\operatorname{diam} C \leq \operatorname{diam} B$

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