Question

Show that $f(x)$, given by $f(x)=x$ for rational and $f(x)=-x$ for irrational numbers, is continuous at $0$

score 371 · Answer 1 · 2026-04-05 12:10:07

371

Views

Show that $f(x)$, given by $f(x)=x$ for rational and $f(x)=-x$ for irrational numbers, is continuous at $0$

Published on 05 Apr 2026 - 12:10

score 109 · Answer 2 · 2017-09-29 09:56:17

109

Views

Rational numbers via equivalent classes

Published on 29 Sep 2017 - 9:56

score 345 · Answer 3 · 2017-09-29 10:03:38

345

Views

Set theory and rational numbers

Published on 29 Sep 2017 - 10:03

score 253 · Answer 4 · 2017-10-02 02:44:09

253

Views

Is a solution of this equation a rational number?

Published on 02 Oct 2017 - 2:44

score 283 · Answer 5 · 2026-03-29 13:52:29

283

Views

Every generating set of $\mathbb{Q}$ as $\mathbb{Z}$-Module has infinite elements

Published on 29 Mar 2026 - 13:52

score 120 · Answer 6 · 2026-04-06 14:41:44

120

Views

Do I need to prove rational number is discontinued on the number axis (irrational numbers are filled in between) and solve this question?

Published on 06 Apr 2026 - 14:41

score 479 · Answer 7 · 2026-04-06 14:40:08

479

Views

Density of a subset of $\mathbb{R}$

Published on 06 Apr 2026 - 14:40

score 76 · Answer 8 · 2017-10-11 18:28:04

76

Views

Why does the definition of a rational number have to include the fact that the denominator is non-zero?

Published on 11 Oct 2017 - 18:28

score 31 · Answer 9 · 2017-10-11 23:25:02

31

Views

Points can be approximated dense in $\mathbb{R}$

Published on 11 Oct 2017 - 23:25

score 430 · Answer 10 · 2017-10-15 18:48:37

430

Views

Prove that $x^3 + y^3 = 9$ has infinitely many rational solutions

Published on 15 Oct 2017 - 18:48

score 2k · Answer 11 · 2017-10-16 04:08:56

2k

Views

Are the polynomials of form $a_0 + a_1x + a_2x^2 +a_3x^3$, with $a_i$ rational, a subspace of $P_3$?

Published on 16 Oct 2017 - 4:08

score 21 · Answer 12 · 2026-04-06 14:41:44

21

Views

Contrapositive of"If $h \in \mathbb Q$ then $\exists a,b \in \mathbb Z$ such that $h=\frac{a}{b}$"

Published on 06 Apr 2026 - 14:41

score 1.4k · Answer 13 · 2026-04-06 14:36:24

1.4k

Views

Is $\sqrt{2}+\sqrt{3}$ rational or irrational?

Published on 06 Apr 2026 - 14:36

score 102 · Answer 14 · 2017-10-17 01:27:18

102

Views

Is $\sum\limits_{i=1}^{+\infty}\frac {1}{q_i+1}$ irrational?

Published on 17 Oct 2017 - 1:27

score 42 · Answer 15 · 2026-04-06 14:37:52

42

Views

Irrationals cannot behave as rationals in this sense, right?

Published on 06 Apr 2026 - 14:37

List Question

Show that $f(x)$, given by $f(x)=x$ for rational and $f(x)=-x$ for irrational numbers, is continuous at $0$

Rational numbers via equivalent classes

Set theory and rational numbers

Is a solution of this equation a rational number?

Every generating set of $\mathbb{Q}$ as $\mathbb{Z}$-Module has infinite elements

Do I need to prove rational number is discontinued on the number axis (irrational numbers are filled in between) and solve this question?

Density of a subset of $\mathbb{R}$

Why does the definition of a rational number have to include the fact that the denominator is non-zero?

Points can be approximated dense in $\mathbb{R}$

Prove that $x^3 + y^3 = 9$ has infinitely many rational solutions

Are the polynomials of form $a_0 + a_1x + a_2x^2 +a_3x^3$, with $a_i$ rational, a subspace of $P_3$?

Contrapositive of"If $h \in \mathbb Q$ then $\exists a,b \in \mathbb Z$ such that $h=\frac{a}{b}$"

Is $\sqrt{2}+\sqrt{3}$ rational or irrational?

Is $\sum\limits_{i=1}^{+\infty}\frac {1}{q_i+1}$ irrational?

Irrationals cannot behave as rationals in this sense, right?

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