Question

For all natural numbers $n$, if $n$ is odd, then $\sqrt{15^n}$ is irrational.

score 93 · Answer 1 · 2026-04-09 04:23:02

93

Views

For all natural numbers $n$, if $n$ is odd, then $\sqrt{15^n}$ is irrational.

Published on 09 Apr 2026 - 4:23

score 31 · Answer 2 · 2022-05-16 07:32:07

31

Views

To whom the properties belong?

Published on 16 May 2022 - 7:32

score 54 · Answer 3 · 2022-05-17 21:03:05

54

Views

Can we always pick an integer power of $e^{i \theta}$ such that its difference with $1$ has rational argument?

Published on 17 May 2022 - 21:03

score 68 · Answer 4 · 2026-04-11 16:41:01

68

Views

Countability of the rationals

Published on 11 Apr 2026 - 16:41

score 80 · Answer 5 · 2022-05-28 17:29:54

80

Views

Most curves in $\mathbb{R}^2$ miss $\mathbb{Q}^2$

Published on 28 May 2022 - 17:29

score 30 · Answer 6 · 2022-06-01 13:30:54

30

Views

If $\text{gcd}(m, n) = d$, true that for $a, m, n \in \mathbb{N}$, $\mathbb{Q}(a^{\frac{1}{n}}, a^{\frac{1}{m}}) = \mathbb{Q}(a^{\frac{d}{nm}})$?

Published on 01 Jun 2022 - 13:30

score 87 · Answer 7 · 2026-04-03 09:28:14

87

Views

Set containing averages of any two numbers of the same set

Published on 03 Apr 2026 - 9:28

score 128 · Answer 8 · 2022-06-07 06:14:44

If $q_1<q_2\in(0,\frac{1}{2})\subset\mathbb{Q}$, then $f(q_1,q_2)=\cos(q_1\pi)-\cos(q_2\pi)$ is bijective between the domain and the image set?

score 213 · Answer 9 · 2026-03-28 10:33:03

213

Views

Why can any open subset $U$ of $\mathbb{Q}^\infty$ be written as disjoint union of basic clopen subsets?

Published on 28 Mar 2026 - 10:33

score 43 · Answer 10 · 2026-04-09 04:21:51

43

Views

Proove verification: $\int_{0}^{1}I_{\omega \notin \mathbb{Q}}(w) d\mathbb{P(\omega )}=1$ using Borel Cantelli lemma

Published on 09 Apr 2026 - 4:21

score 99 · Answer 11 · 2026-04-10 21:27:42

99

Views

Why are rational numbers $\sigma$-compact?

Published on 10 Apr 2026 - 21:27

score 57 · Answer 12 · 2026-04-07 01:01:16

57

Views

Finding the biggest $k\leq k_0$ such that the interval $k[A, B]$ contains an integer

Published on 07 Apr 2026 - 1:01

score 89 · Answer 13 · 2026-03-26 10:58:38

89

Views

Hamel basis and real algebraic numbers

Published on 26 Mar 2026 - 10:58

score 87 · Answer 14 · 2026-04-10 00:07:17

87

Views

Apparent contradiction in the definition of a Dedekind cuts

Published on 10 Apr 2026 - 0:07

score 29 · Answer 15 · 2026-04-10 16:42:38

29

Views

Total Order on a subset of Rationals according to their "Simplicity"

Published on 10 Apr 2026 - 16:42

List Question

For all natural numbers $n$, if $n$ is odd, then $\sqrt{15^n}$ is irrational.

To whom the properties belong?

Can we always pick an integer power of $e^{i \theta}$ such that its difference with $1$ has rational argument?

Countability of the rationals

Most curves in $\mathbb{R}^2$ miss $\mathbb{Q}^2$

If $\text{gcd}(m, n) = d$, true that for $a, m, n \in \mathbb{N}$, $\mathbb{Q}(a^{\frac{1}{n}}, a^{\frac{1}{m}}) = \mathbb{Q}(a^{\frac{d}{nm}})$?

Set containing averages of any two numbers of the same set

If $q_1<q_2\in(0,\frac{1}{2})\subset\mathbb{Q}$, then $f(q_1,q_2)=\cos(q_1\pi)-\cos(q_2\pi)$ is bijective between the domain and the image set?

Why can any open subset $U$ of $\mathbb{Q}^\infty$ be written as disjoint union of basic clopen subsets?

Proove verification: $\int_{0}^{1}I_{\omega \notin \mathbb{Q}}(w) d\mathbb{P(\omega )}=1$ using Borel Cantelli lemma

Why are rational numbers $\sigma$-compact?

Finding the biggest $k\leq k_0$ such that the interval $k[A, B]$ contains an integer

Hamel basis and real algebraic numbers

Apparent contradiction in the definition of a Dedekind cuts

Total Order on a subset of Rationals according to their "Simplicity"

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