Question

Is $\sum_{k=1}^{\infty} 1/k^2 = \pi^2/6$ a valid example for the incompleteness of rational numbers?

score 83 · Answer 1 · 2026-04-11 23:15:54

83

Views

Is $\sum_{k=1}^{\infty} 1/k^2 = \pi^2/6$ a valid example for the incompleteness of rational numbers?

Published on 11 Apr 2026 - 23:15

score 42 · Answer 2 · 2022-12-04 02:42:39

42

Views

Help understanding rational proof given three rationals $x,y,z$ if $x = z$ and $y = z$ then $x =y$

Published on 04 Dec 2022 - 2:42

score 144 · Answer 3 · 2026-04-11 20:33:10

144

Views

Is $\mathbb{R} \setminus \mathbb{Q}$ connected?

Published on 11 Apr 2026 - 20:33

score 80 · Answer 4 · 2026-04-09 13:29:59

80

Views

Can both of $(x+1)(x+3)$ and $(x-1)(x-3)$ are rational numbers imply $(x+1)^2$ is rational?

Published on 09 Apr 2026 - 13:29

score 69 · Answer 5 · 2022-12-12 10:34:16

69

Views

find $u < r$, $v < s$ such that $p< uv < rs$

Published on 12 Dec 2022 - 10:34

score 130 · Answer 6 · 2026-04-07 09:47:42

130

Views

Non-trivial intersection of two cyclic groups

Published on 07 Apr 2026 - 9:47

score 118 · Answer 7 · 2022-12-18 22:10:13

118

Views

Separating rational coefficients from $a + b\sqrt{2}$

Published on 18 Dec 2022 - 22:10

score 142 · Answer 8 · 2026-04-11 17:48:32

142

Views

Rational approximation of $\pi$ by recursion

Published on 11 Apr 2026 - 17:48

score 132 · Answer 9 · 2022-12-23 16:53:15

132

Views

Definition of closed and open "Qanifolds" (manifolds over $\mathbb{Q}$): can a Qanifold be both closed and open?

Published on 23 Dec 2022 - 16:53

score 198 · Answer 10 · 2022-12-24 03:38:04

198

Views

Continuous bijection from $(0,1]$ to $(0,1)$ on rational numbers.

Published on 24 Dec 2022 - 3:38

score 191 · Answer 11 · 2022-12-24 16:32:52

191

Views

Continuous bijection from $(0,1]$ to $(0,1)$ on rational numbers with a continuous inverse.

Published on 24 Dec 2022 - 16:32

score 106 · Answer 12 · 2022-12-24 18:48:18

106

Views

Continuous bijection from $[0,1]$ to $(0,1)$ on rational numbers with a continuous inverse.

Published on 24 Dec 2022 - 18:48

score 157 · Answer 13 · 2023-01-02 02:32:19

157

Views

What elements would need to be added to the rationals for it to be closed under exponentiation?

Published on 02 Jan 2023 - 2:32

score 190 · Answer 14 · 2026-03-29 14:20:20

190

Views

Show that there is no right triangle whose legs are rational numbers and whose hypotenuse is $\sqrt{2022}$.

Published on 29 Mar 2026 - 14:20

score 53 · Answer 15 · 2026-04-09 13:29:07

53

Views

Does a Lipschitz continuous surjection $f:\mathbb R \setminus \mathbb Q \to \mathbb Q$ exist?

Published on 09 Apr 2026 - 13:29

List Question

Is $\sum_{k=1}^{\infty} 1/k^2 = \pi^2/6$ a valid example for the incompleteness of rational numbers?

Help understanding rational proof given three rationals $x,y,z$ if $x = z$ and $y = z$ then $x =y$

Is $\mathbb{R} \setminus \mathbb{Q}$ connected?

Can both of $(x+1)(x+3)$ and $(x-1)(x-3)$ are rational numbers imply $(x+1)^2$ is rational?

find $u < r$, $v < s$ such that $p< uv < rs$

Non-trivial intersection of two cyclic groups

Separating rational coefficients from $a + b\sqrt{2}$

Rational approximation of $\pi$ by recursion

Definition of closed and open "Qanifolds" (manifolds over $\mathbb{Q}$): can a Qanifold be both closed and open?

Continuous bijection from $(0,1]$ to $(0,1)$ on rational numbers.

Continuous bijection from $(0,1]$ to $(0,1)$ on rational numbers with a continuous inverse.

Continuous bijection from $[0,1]$ to $(0,1)$ on rational numbers with a continuous inverse.

What elements would need to be added to the rationals for it to be closed under exponentiation?

Show that there is no right triangle whose legs are rational numbers and whose hypotenuse is $\sqrt{2022}$.

Does a Lipschitz continuous surjection $f:\mathbb R \setminus \mathbb Q \to \mathbb Q$ exist?

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