Question

If $b \in \mathbb{R}\setminus \mathbb{Q}$ then are there $h$ very close to $0$ such that $b+h \in \mathbb{Q}$?

score 45 · Answer 1 · 2026-04-07 21:23:25

45

Views

If $b \in \mathbb{R}\setminus \mathbb{Q}$ then are there $h$ very close to $0$ such that $b+h \in \mathbb{Q}$?

Published on 07 Apr 2026 - 21:23

score 33 · Answer 2 · 2020-10-23 12:37:53

33

Views

Show that a set of open intervals can be formed by the countable union of sequences of rationals.

Published on 23 Oct 2020 - 12:37

score 207 · Answer 3 · 2026-04-07 21:20:58

207

Views

Prove that there is no rational lowest upper bound for $\sqrt{3}$.

Published on 07 Apr 2026 - 21:20

score 526 · Answer 4 · 2020-10-25 06:21:20

526

Views

Prove that $\mathbb{Q}^n$ is a countable dense set in $\mathbb{R}^n$

Published on 25 Oct 2020 - 6:21

score 117 · Answer 5 · 2026-03-28 16:58:05

117

Views

Number of group homomorphism from the group $D_8$ to $\Bbb Q^{\times} $

Published on 28 Mar 2026 - 16:58

score 39 · Answer 6 · 2026-04-07 21:24:10

39

Views

Measure of the set $x\in [0,1]$ such that $|x-p/q|>(Aq^2)^{-1}$ for any rational $p/q$

Published on 07 Apr 2026 - 21:24

score 67 · Answer 7 · 2020-10-29 19:23:23

67

Views

Prove that there is no rational $x$ such that $x-1 = 1/x$

Published on 29 Oct 2020 - 19:23

score 589 · Answer 8 · 2026-04-08 11:39:08

589

Views

From $3$ chocolate bars we can make at most $5$ chocolate rabbits. What is the greatest number of rabbits that can be made from $16$ bars?

Published on 08 Apr 2026 - 11:39

score 117 · Answer 9 · 2026-04-08 11:34:55

117

Views

Proving that rational numbers cannot have denominator zero (without referring to division by zero)

Published on 08 Apr 2026 - 11:34

score 154 · Answer 10 · 2026-04-07 21:23:34

154

Views

Some alternative examples to the question "Are there two irrational numbers $x$ and $y$ such that $x^y$ is rational?"

Published on 07 Apr 2026 - 21:23

score 161 · Answer 11 · 2026-04-07 22:57:55

161

Views

Prove that $\sqrt[3]{2}+\sqrt[3]{4}$ is irrational

Published on 07 Apr 2026 - 22:57

score 48 · Answer 12 · 2020-11-03 17:57:31

48

Views

Proof a function is injective - (intermediary step to proving the rationals are countable)

Published on 03 Nov 2020 - 17:57

score 264 · Answer 13 · 2020-11-04 17:39:12

264

Views

Give an open cover of $[0,1]\cap\mathbb{Q}$ that has no finite subcover

Published on 04 Nov 2020 - 17:39

score 113 · Answer 14 · 2020-11-07 16:09:51

113

Views

Does the definition of rational numbers already assumes an understanding of them?

Published on 07 Nov 2020 - 16:09

score 1k · Answer 15 · 2026-04-05 18:23:35

1k

Views

Proof that $\mathbb Q$ is not cyclic.

Published on 05 Apr 2026 - 18:23

List Question

If $b \in \mathbb{R}\setminus \mathbb{Q}$ then are there $h$ very close to $0$ such that $b+h \in \mathbb{Q}$?

Show that a set of open intervals can be formed by the countable union of sequences of rationals.

Prove that there is no rational lowest upper bound for $\sqrt{3}$.

Prove that $\mathbb{Q}^n$ is a countable dense set in $\mathbb{R}^n$

Number of group homomorphism from the group $D_8$ to $\Bbb Q^{\times} $

Measure of the set $x\in [0,1]$ such that $|x-p/q|>(Aq^2)^{-1}$ for any rational $p/q$

Prove that there is no rational $x$ such that $x-1 = 1/x$

From $3$ chocolate bars we can make at most $5$ chocolate rabbits. What is the greatest number of rabbits that can be made from $16$ bars?

Proving that rational numbers cannot have denominator zero (without referring to division by zero)

Some alternative examples to the question "Are there two irrational numbers $x$ and $y$ such that $x^y$ is rational?"

Prove that $\sqrt[3]{2}+\sqrt[3]{4}$ is irrational

Proof a function is injective - (intermediary step to proving the rationals are countable)

Give an open cover of $[0,1]\cap\mathbb{Q}$ that has no finite subcover

Does the definition of rational numbers already assumes an understanding of them?

Proof that $\mathbb Q$ is not cyclic.

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