Question

Proof that any upper bound of $(0, \sqrt 2]$ has to be greater than $\sqrt 2$ in the domain of rationals.

score 176 · Answer 1 · 2026-04-09 07:59:47

176

Views

Proof that any upper bound of $(0, \sqrt 2]$ has to be greater than $\sqrt 2$ in the domain of rationals.

Published on 09 Apr 2026 - 7:59

score 123 · Answer 2 · 2026-04-09 07:59:47

123

Views

Why does the sum of reciprocals of squares converge to an irrational number?

Published on 09 Apr 2026 - 7:59

score 70 · Answer 3 · 2022-10-07 13:11:14

70

Views

What is the name of the following theorem used to prove that rationals are not complete?

Published on 07 Oct 2022 - 13:11

score 75 · Answer 4 · 2026-04-01 09:45:28

75

Views

Why does this not disprove that the set of all rational numbers is countable?

Published on 01 Apr 2026 - 9:45

score 158 · Answer 5 · 2026-04-01 08:09:02

158

Views

Flaw in my proof that $\mathbb Q$ is countable?

Published on 01 Apr 2026 - 8:09

score 116 · Answer 6 · 2022-10-13 17:52:46

116

Views

Does the set of rational numbers include repeating values?

Published on 13 Oct 2022 - 17:52

score 132 · Answer 7 · 2026-04-09 11:38:51

132

Views

Prove $\sqrt{\frac32}$ is irrational

Published on 09 Apr 2026 - 11:38

score 226 · Answer 8 · 2022-10-23 13:19:01

226

Views

Prove that for every $x<y\in \mathbb{R}$ there is a rational number in the interval $(x,y)$

Published on 23 Oct 2022 - 13:19

score 97 · Answer 9 · 2026-04-12 02:17:43

97

Views

Spivak, Calculus: how to show that $a^x<a^y$ for $a>1$ and $a^x>a^y$ for $a<1$, using the "usual algebraic definition" of $a^x$ for rational $x$.

Published on 12 Apr 2026 - 2:17

score 143 · Answer 10 · 2026-04-11 21:42:20

143

Views

Why is the function $f(x) = e^x$ not a rational function?

Published on 11 Apr 2026 - 21:42

score 88 · Answer 11 · 2026-04-11 03:44:31

88

Views

What it means? How to solved it?

Published on 11 Apr 2026 - 3:44

score 100 · Answer 12 · 2026-03-27 14:52:45

100

Views

Prove that number $\sqrt{2}$ is an irrational number using this theorem "if $a^2$ is even, $a$ must be even"

Published on 27 Mar 2026 - 14:52

score 372 · Answer 13 · 2026-03-28 12:34:09

372

Views

What is the smallest infinite field?

Published on 28 Mar 2026 - 12:34

score 122 · Answer 14 · 2026-04-11 11:12:43

122

Views

Splitting a rectangle into MxN pieces, with target aspect ratio

Published on 11 Apr 2026 - 11:12

score 45 · Answer 15 · 2026-04-09 11:37:08

45

Views

Am I right with this limit?

Published on 09 Apr 2026 - 11:37

List Question

Proof that any upper bound of $(0, \sqrt 2]$ has to be greater than $\sqrt 2$ in the domain of rationals.

Why does the sum of reciprocals of squares converge to an irrational number?

What is the name of the following theorem used to prove that rationals are not complete?

Why does this not disprove that the set of all rational numbers is countable?

Flaw in my proof that $\mathbb Q$ is countable?

Does the set of rational numbers include repeating values?

Prove $\sqrt{\frac32}$ is irrational

Prove that for every $x<y\in \mathbb{R}$ there is a rational number in the interval $(x,y)$

Spivak, Calculus: how to show that $a^x<a^y$ for $a>1$ and $a^x>a^y$ for $a<1$, using the "usual algebraic definition" of $a^x$ for rational $x$.

Why is the function $f(x) = e^x$ not a rational function?

What it means? How to solved it?

Prove that number $\sqrt{2}$ is an irrational number using this theorem "if $a^2$ is even, $a$ must be even"

What is the smallest infinite field?

Splitting a rectangle into MxN pieces, with target aspect ratio

Am I right with this limit?

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