Question

What is a point in $\mathbb{R}^2\setminus \mathbb{Q}^2$ that only has one irrational coordinate?

score 101 · Answer 1 · 2016-08-04 02:33:55

101

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What is a point in $\mathbb{R}^2\setminus \mathbb{Q}^2$ that only has one irrational coordinate?

Published on 04 Aug 2016 - 2:33

score 69 · Answer 2 · 2016-08-06 17:35:56

69

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Prove or disprove: For every number $s \in \mathbb{R} \setminus \mathbb{Q}$ there is a $t \in \mathbb{R}$ with $s+t \in \mathbb{Q}$

Published on 06 Aug 2016 - 17:35

score 365 · Answer 3 · 2026-03-26 04:16:08

365

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Approximation of integer by multiple of irrational number

Published on 26 Mar 2026 - 4:16

score 3.8k · Answer 4 · 2016-08-08 08:03:48

3.8k

Views

Prove that $\sqrt{2}+\sqrt{3}$ is irrational.

Published on 08 Aug 2016 - 8:03

score 2k · Answer 5 · 2016-08-08 22:05:57

2k

Views

Proof of the irrationality of cube root 16

Published on 08 Aug 2016 - 22:05

score 342 · Answer 6 · 2016-08-12 03:32:11

342

Views

$-1$ raised to the $\pi$

Published on 12 Aug 2016 - 3:32

score 328 · Answer 7 · 2026-03-26 23:09:16

328

Views

Intuition behind irrationality of $\pi$

Published on 26 Mar 2026 - 23:09

score 276 · Answer 8 · 2026-03-26 17:52:37

276

Views

Can you provide an example where a rational power irrational number is rational?

Published on 26 Mar 2026 - 17:52

score 320 · Answer 9 · 2016-08-15 09:06:45

320

Views

Irrationals yet as ordered pairs of rationals?

Published on 15 Aug 2016 - 9:06

score 1.7k · Answer 10 · 2016-08-16 05:36:38

1.7k

Views

Are all numbers rational?

Published on 16 Aug 2016 - 5:36

score 236 · Answer 11 · 2016-08-16 19:36:04

236

Views

How often is $a^b$ rational when $a,b>0$ are irrational.

Published on 16 Aug 2016 - 19:36

score 577 · Answer 12 · 2016-08-20 21:03:50

577

Views

Deducing $\pi$ is irrational from the form of a polynomial in $\pi$.

Published on 20 Aug 2016 - 21:03

score 1.3k · Answer 13 · 2026-03-26 23:10:56

1.3k

Views

Why are the continued fractions of non-square-root numbers ($\sqrt[a]{x}$ where $a>2$) not periodic?

Published on 26 Mar 2026 - 23:10

score 1.4k · Answer 14 · 2016-08-21 17:08:55

1.4k

Views

Is the difference of two irrationals which are each contained under a single square root irrational?

Published on 21 Aug 2016 - 17:08

score 8.5k · Answer 15 · 2026-03-26 18:59:05

8.5k

Views

How irrational quantities physically exist in nature?

Published on 26 Mar 2026 - 18:59

List Question

What is a point in $\mathbb{R}^2\setminus \mathbb{Q}^2$ that only has one irrational coordinate?

Prove or disprove: For every number $s \in \mathbb{R} \setminus \mathbb{Q}$ there is a $t \in \mathbb{R}$ with $s+t \in \mathbb{Q}$

Approximation of integer by multiple of irrational number

Prove that $\sqrt{2}+\sqrt{3}$ is irrational.

Proof of the irrationality of cube root 16

$-1$ raised to the $\pi$

Intuition behind irrationality of $\pi$

Can you provide an example where a rational power irrational number is rational?

Irrationals yet as ordered pairs of rationals?

Are all numbers rational?

How often is $a^b$ rational when $a,b>0$ are irrational.

Deducing $\pi$ is irrational from the form of a polynomial in $\pi$.

Why are the continued fractions of non-square-root numbers ($\sqrt[a]{x}$ where $a>2$) not periodic?

Is the difference of two irrationals which are each contained under a single square root irrational?

How irrational quantities physically exist in nature?

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