Question

Proving the negation of a conditional using proof by contradiction

score 165 · Answer 1 · 2019-04-08 10:21:31

165

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Proving the negation of a conditional using proof by contradiction

Published on 08 Apr 2019 - 10:21

score 1.1k · Answer 2 · 2019-04-08 12:13:03

1.1k

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Suppose that $x$ and $y$ are irrational, but $x + y$ is rational. Prove that $x -y$ is irrational.

Published on 08 Apr 2019 - 12:13

score 1.7k · Answer 3 · 2026-03-28 02:09:28

1.7k

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What is $\mathbb{Q}$?

Published on 28 Mar 2026 - 2:09

score 477 · Answer 4 · 2026-03-26 01:04:36

477

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Prob. 1, Sec. 29, in Munkres' TOPOLOGY, 2nd ed: The subspace $\mathbb{Q}$ of $\mathbb{R}$ is not locally compact

Published on 26 Mar 2026 - 1:04

score 424 · Answer 5 · 2026-03-26 12:54:02

424

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Are there $2^{\aleph_{0} }$ sets of natural numbers such that each two have finite intersection

Published on 26 Mar 2026 - 12:54

score 371 · Answer 6 · 2026-03-27 15:19:02

371

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Famous fractions: Can any "special" numbers be approximated by simple ratios like $3.14\ldots$ as $22/7$?

Published on 27 Mar 2026 - 15:19

score 27 · Answer 7 · 2026-03-25 22:10:39

27

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Can we fill the plane with a certain operation?

Published on 25 Mar 2026 - 22:10

score 57 · Answer 8 · 2019-04-26 05:14:19

57

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Prove that $a$ and $b$ are rational numbers

Published on 26 Apr 2019 - 5:14

score 522 · Answer 9 · 2019-04-26 14:35:26

522

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Numerator and denominator of rational number

Published on 26 Apr 2019 - 14:35

score 94 · Answer 10 · 2019-05-03 06:34:36

94

Views

Are Rationals constructed from infinite Naturals valid?

Published on 03 May 2019 - 6:34

score 39 · Answer 11 · 2019-05-08 01:31:33

39

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What numbers can be approximated by ratios of numbers containing only specified digits?

Published on 08 May 2019 - 1:31

score 162 · Answer 12 · 2026-03-26 16:56:55

162

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Alternation of Rationals and Irrationals?

Published on 26 Mar 2026 - 16:56

score 210 · Answer 13 · 2019-05-20 15:41:43

210

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Prove that $f(x) = x$ when $x$ is rational and $f(x) = 1 - x$ when $x$ is irrational is continuous at $x = \frac{1}{2}$.

Published on 20 May 2019 - 15:41

score 118 · Answer 14 · 2019-05-20 20:29:49

118

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Proof of Density of Rational Numbers as given in Howie

Published on 20 May 2019 - 20:29

score 134 · Answer 15 · 2019-05-24 00:19:05

134

Views

Rudin's proof of theorem 1.20b (Archimedean Principle)

Published on 24 May 2019 - 0:19

List Question

Proving the negation of a conditional using proof by contradiction

Suppose that $x$ and $y$ are irrational, but $x + y$ is rational. Prove that $x -y$ is irrational.

What is $\mathbb{Q}$?

Prob. 1, Sec. 29, in Munkres' TOPOLOGY, 2nd ed: The subspace $\mathbb{Q}$ of $\mathbb{R}$ is not locally compact

Are there $2^{\aleph_{0} }$ sets of natural numbers such that each two have finite intersection

Famous fractions: Can any "special" numbers be approximated by simple ratios like $3.14\ldots$ as $22/7$?

Can we fill the plane with a certain operation?

Prove that $a$ and $b$ are rational numbers

Numerator and denominator of rational number

Are Rationals constructed from infinite Naturals valid?

What numbers can be approximated by ratios of numbers containing only specified digits?

Alternation of Rationals and Irrationals?

Prove that $f(x) = x$ when $x$ is rational and $f(x) = 1 - x$ when $x$ is irrational is continuous at $x = \frac{1}{2}$.

Proof of Density of Rational Numbers as given in Howie

Rudin's proof of theorem 1.20b (Archimedean Principle)

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