Question

Proof for number of rational ordered pairs on a line

score 131 · Answer 1 · 2015-02-14 19:29:14

131

Views

Proof for number of rational ordered pairs on a line

Published on 14 Feb 2015 - 19:29

score 206 · Answer 2 · 2026-04-02 19:00:09

206

Views

Let $S=\{x\in\mathbb Q\mid x>2\}$. Prove $\inf S = 2$.

Published on 02 Apr 2026 - 19:00

score 115 · Answer 3 · 2015-02-16 10:16:13

115

Views

Algebraic number with bounded coefficients

Published on 16 Feb 2015 - 10:16

score 96 · Answer 4 · 2026-04-03 04:48:28

96

Views

Find the functions

Published on 03 Apr 2026 - 4:48

score 36 · Answer 5 · 2015-02-24 21:12:26

36

Views

A Elementary fact but proof needed

Published on 24 Feb 2015 - 21:12

score 353 · Answer 6 · 2015-02-26 13:09:25

353

Views

Finding a sequence of sets whose intersection is a null set

Published on 26 Feb 2015 - 13:09

score 100 · Answer 7 · 2026-03-28 22:31:11

100

Views

for $p$ given, $\zeta_p$ a primitive root of unity, fow which $d\in \mathbb{Z}$ does $\zeta_p \in \mathbb{Q}(\sqrt{d})$?

Published on 28 Mar 2026 - 22:31

score 4.3k · Answer 8 · 2026-03-27 06:12:40

4.3k

Views

Are there any bases which represent all rationals in a finite number of digits?

Published on 27 Mar 2026 - 6:12

score 1.9k · Answer 9 · 2026-04-03 06:18:12

1.9k

Views

If $ f(x \cdot f(y) + f(x)) = y \cdot f(x) + x $, then $f(x)=x$

Published on 03 Apr 2026 - 6:18

score 1.5k · Answer 10 · 2026-03-26 05:56:00

1.5k

Views

Show using ordering axioms that $x^2 < y^2$ for $x, y \in \mathbb{Q}$, with $0 < x < y$

Published on 26 Mar 2026 - 5:56

score 87 · Answer 11 · 2026-03-30 01:30:56

87

Views

$a, b, x \in \mathbb{Q}$ with $a \neq 0$. Is the $\frac{b}{a}$ the only possible value for x in $a \cdot x = b$

Published on 30 Mar 2026 - 1:30

score 71 · Answer 12 · 2026-03-30 20:44:06

71

Views

Simplifying $\frac{1/(\frac{1}{z_1}(1-t)+\frac{1}{z_2}t) - z_1}{(z_2 - z_1)}$

Published on 30 Mar 2026 - 20:44

score 3k · Answer 13 · 2015-03-06 00:57:13

3k

Views

Prove that the numbers of the form $a+b\sqrt{2}$, where $a$ and $b$ are rational numbers, form a subfield of $\mathbb{C}$.

Published on 06 Mar 2015 - 0:57

score 474 · Answer 14 · 2015-03-07 00:21:16

474

Views

There does not exist rational numbers $x$ and $y$ such that $x^y$ is a positive integer and $y^x$ is a negative integer

Published on 07 Mar 2015 - 0:21

score 48 · Answer 15 · 2015-03-08 13:01:17

48

Views

Not including rational number in inequality

Published on 08 Mar 2015 - 13:01

List Question

Proof for number of rational ordered pairs on a line

Let $S=\{x\in\mathbb Q\mid x>2\}$. Prove $\inf S = 2$.

Algebraic number with bounded coefficients

Find the functions

A Elementary fact but proof needed

Finding a sequence of sets whose intersection is a null set

for $p$ given, $\zeta_p$ a primitive root of unity, fow which $d\in \mathbb{Z}$ does $\zeta_p \in \mathbb{Q}(\sqrt{d})$?

Are there any bases which represent all rationals in a finite number of digits?

If $ f(x \cdot f(y) + f(x)) = y \cdot f(x) + x $, then $f(x)=x$

Show using ordering axioms that $x^2 < y^2$ for $x, y \in \mathbb{Q}$, with $0 < x < y$

$a, b, x \in \mathbb{Q}$ with $a \neq 0$. Is the $\frac{b}{a}$ the only possible value for x in $a \cdot x = b$

Simplifying $\frac{1/(\frac{1}{z_1}(1-t)+\frac{1}{z_2}t) - z_1}{(z_2 - z_1)}$

Prove that the numbers of the form $a+b\sqrt{2}$, where $a$ and $b$ are rational numbers, form a subfield of $\mathbb{C}$.

There does not exist rational numbers $x$ and $y$ such that $x^y$ is a positive integer and $y^x$ is a negative integer

Not including rational number in inequality

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