Question

For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$

score 6k · Answer 1 · 2026-05-11 03:13:29

6k

Views

For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$

Published on 11 May 2026 - 3:13

score 78 · Answer 2 · 2026-04-14 03:34:40

78

Views

Solving surds without compairing

Published on 14 Apr 2026 - 3:34

score 320 · Answer 3 · 2026-04-14 12:04:40

320

Views

is $(\mathbb{Q} \times (\mathbb{R}\setminus\mathbb{Q}))\cup((\mathbb{R}\setminus\mathbb{Q})\times\mathbb{Q})$ connected? path connected?

Published on 14 Apr 2026 - 12:04

score 2.6k · Answer 4 · 2026-04-10 14:19:30

2.6k

Views

Why there are irrational numbers?

Published on 10 Apr 2026 - 14:19

score 69 · Answer 5 · 2026-04-13 23:18:48

69

Views

"Building blocks" for computable functions

Published on 13 Apr 2026 - 23:18

score 69 · Answer 6 · 2026-04-15 18:35:14

69

Views

negative powers $(x^{-2} = 1/x^2)$

Published on 15 Apr 2026 - 18:35

score 1.4k · Answer 7 · 2026-05-11 07:52:23

1.4k

Views

Real numbers that are not the roots of any polynomial equation with algebraic coefficients

Published on 11 May 2026 - 7:52

score 598 · Answer 8 · 2026-04-14 16:06:24

598

Views

Can we prove that the solutions of $\int_0^y \sin(\sin(x)) dx =1$ are irrational?

Published on 14 Apr 2026 - 16:06

score 450 · Answer 9 · 2026-04-10 13:53:33

450

Views

Irrationality measure.

Published on 10 Apr 2026 - 13:53

score 810 · Answer 10 · 2026-04-11 06:02:42

810

Views

How to prove that $\cos(n)$ is irrational?

Published on 11 Apr 2026 - 6:02

score 260 · Answer 11 · 2026-04-11 04:14:10

260

Views

Does the limit of a sequence with floor function exist?

Published on 11 Apr 2026 - 4:14

score 1.6k · Answer 12 · 2026-04-17 16:01:52

1.6k

Views

Prove that if $n \geq 2$, then $\sqrt[n]{n}$ is irrational. Hint, show that if $n \geq 2$, then $2^{n} > n$.

Published on 17 Apr 2026 - 16:01

score 1.2k · Answer 13 · 2026-04-11 00:26:30

1.2k

Views

Is the fact that there are more irrational numbers than rational numbers useful?

Published on 11 Apr 2026 - 0:26

score 887 · Answer 14 · 2026-04-16 02:09:16

887

Views

Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$

Published on 16 Apr 2026 - 2:09

score 2.1k · Answer 15 · 2026-04-13 16:16:24

2.1k

Views

Conjecture: if $a+b$ and $ab$ are rational, $a$ and $b$ are rational

Published on 13 Apr 2026 - 16:16

List Question

For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$

Solving surds without compairing

is $(\mathbb{Q} \times (\mathbb{R}\setminus\mathbb{Q}))\cup((\mathbb{R}\setminus\mathbb{Q})\times\mathbb{Q})$ connected? path connected?

Why there are irrational numbers?

"Building blocks" for computable functions

negative powers $(x^{-2} = 1/x^2)$

Real numbers that are not the roots of any polynomial equation with algebraic coefficients

Can we prove that the solutions of $\int_0^y \sin(\sin(x)) dx =1$ are irrational?

Irrationality measure.

How to prove that $\cos(n)$ is irrational?

Does the limit of a sequence with floor function exist?

Prove that if $n \geq 2$, then $\sqrt[n]{n}$ is irrational. Hint, show that if $n \geq 2$, then $2^{n} > n$.

Is the fact that there are more irrational numbers than rational numbers useful?

Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$

Conjecture: if $a+b$ and $ab$ are rational, $a$ and $b$ are rational

Trending Questions

Popular # Hahtags

Popular Questions