Question

Asymptotic Behaviour of Rational Approximations of an Irrational Real Number

score 65 · Answer 1 · 2026-03-25 16:03:54

65

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Asymptotic Behaviour of Rational Approximations of an Irrational Real Number

Published on 25 Mar 2026 - 16:03

score 161 · Answer 2 · 2016-08-23 09:15:39

161

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$\exists r\in \mathbb{Q}$ such that $\forall s\in\overline{\mathbb{Q}}$, $rs\in\mathbb{Q}$

Published on 23 Aug 2016 - 9:15

score 98 · Answer 3 · 2026-03-29 15:02:23

98

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series with irrational numbers

Published on 29 Mar 2026 - 15:02

score 12.2k · Answer 4 · 2016-08-28 08:42:16

12.2k

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If $a+b+c=0$ then the roots of $ax^2+bx+c=0$ are rational?

Published on 28 Aug 2016 - 8:42

score 287 · Answer 5 · 2026-02-23 05:36:13

287

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Surprising continued fractions of numbers in the form $\sum_{n=0}^\infty \frac{1}{a^{2^n}}$, including the same pattern for every $a>2$

Published on 23 Feb 2026 - 5:36

score 288 · Answer 6 · 2016-08-31 01:27:52

288

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For any irrational number $r$, $r^2$ is irrational

Published on 31 Aug 2016 - 1:27

score 101 · Answer 7 · 2016-08-31 13:20:59

101

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Does there exist a positive irrational number $\alpha$, the number $\lfloor n\alpha \rfloor$ is never a prime?

Published on 31 Aug 2016 - 13:20

score 515 · Answer 8 · 2026-03-27 13:25:36

515

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Can this "formal proof" of irrationality of $\pi$ be made rigorous?

Published on 27 Mar 2026 - 13:25

score 427 · Answer 9 · 2026-02-23 05:32:47

427

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Numbers $p-\sqrt{q}$ having regular egyptian fraction expansions?

Published on 23 Feb 2026 - 5:32

score 273 · Answer 10 · 2016-09-01 13:56:34

273

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Beautiful 'folding' pattern in the decimal expansion of $\sum_{n=0}^\infty \frac{1}{10^{2^n}-1}=\frac{1}{9}+\frac{1}{99}+\frac{1}{9999}+\dots$

Published on 01 Sep 2016 - 13:56

score 145 · Answer 11 · 2016-09-02 22:10:37

145

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Proof there is a irrational number $r$ in $a < b$ so that $a < r < b$

Published on 02 Sep 2016 - 22:10

score 13.5k · Answer 12 · 2016-09-06 06:40:31

13.5k

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Is there a "positive" definition for irrational numbers?

Published on 06 Sep 2016 - 6:40

score 238 · Answer 13 · 2016-09-06 18:21:23

238

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Equivalent definition for irrational numbers

Published on 06 Sep 2016 - 18:21

score 15.3k · Answer 14 · 2016-09-06 22:28:58

15.3k

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Prove that there is an irrational number and a rational number between any two distinct real numbers

Published on 06 Sep 2016 - 22:28

score 157 · Answer 15 · 2026-03-27 15:36:18

157

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Irrationality of the Riemann zeta-function on odd arguments

Published on 27 Mar 2026 - 15:36

List Question

Asymptotic Behaviour of Rational Approximations of an Irrational Real Number

$\exists r\in \mathbb{Q}$ such that $\forall s\in\overline{\mathbb{Q}}$, $rs\in\mathbb{Q}$

series with irrational numbers

If $a+b+c=0$ then the roots of $ax^2+bx+c=0$ are rational?

Surprising continued fractions of numbers in the form $\sum_{n=0}^\infty \frac{1}{a^{2^n}}$, including the same pattern for every $a>2$

For any irrational number $r$, $r^2$ is irrational

Does there exist a positive irrational number $\alpha$, the number $\lfloor n\alpha \rfloor$ is never a prime?

Can this "formal proof" of irrationality of $\pi$ be made rigorous?

Numbers $p-\sqrt{q}$ having regular egyptian fraction expansions?

Beautiful 'folding' pattern in the decimal expansion of $\sum_{n=0}^\infty \frac{1}{10^{2^n}-1}=\frac{1}{9}+\frac{1}{99}+\frac{1}{9999}+\dots$

Proof there is a irrational number $r$ in $a < b$ so that $a < r < b$

Is there a "positive" definition for irrational numbers?

Equivalent definition for irrational numbers

Prove that there is an irrational number and a rational number between any two distinct real numbers

Irrationality of the Riemann zeta-function on odd arguments

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