Question

How to calculate the cardinality of the complement of two countable sets of reals?

score 463 · Answer 1 · 2015-08-21 21:08:14

463

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How to calculate the cardinality of the complement of two countable sets of reals?

Published on 21 Aug 2015 - 21:08

score 67 · Answer 2 · 2026-03-31 23:29:24

67

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Let $\Gamma$ be a $\kappa$-based monotone operator where $\kappa$ is regular. Then the closure ordinal of $\Gamma$ is $\kappa$.

Published on 31 Mar 2026 - 23:29

score 68 · Answer 3 · 2015-08-22 15:37:39

68

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basis for $\mathbb{R}^{\mathbb{N}}:=\left\{f:\mathbb{N}\to\mathbb{R}\right\}$, and its cardinality.

Published on 22 Aug 2015 - 15:37

score 424 · Answer 4 · 2015-08-28 10:18:58

424

Views

How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?

Published on 28 Aug 2015 - 10:18

score 174 · Answer 5 · 2015-08-28 17:00:13

174

Views

Characterizing uncountable connected topological spaces

Published on 28 Aug 2015 - 17:00

score 42 · Answer 6 · 2015-08-30 10:13:29

42

Views

proving $|X|<|Y|$, $|Y|<|Z| \Longrightarrow |X|<|Z|$ without CSB

Published on 30 Aug 2015 - 10:13

score 221 · Answer 7 · 2015-08-31 18:42:40

221

Views

Give an example of a structure of cardinality $\omega_2$ that has a substructure of $\omega$ but no substructure of $\omega_1$

Published on 31 Aug 2015 - 18:42

score 52 · Answer 8 · 2026-04-03 07:34:53

52

Views

Does every set have choice sequences as long as the original set?

Published on 03 Apr 2026 - 7:34

score 2k · Answer 9 · 2015-09-01 14:56:24

2k

Views

Prove that the set of all periodic sequences (from some index) of natural numbers is countable

Published on 01 Sep 2015 - 14:56

score 30 · Answer 10 · 2015-09-02 08:46:15

30

Views

Prove that if $|X|=\aleph _0$ then there exist a family of sets, $\mathcal{F}$, of subsets of $X$, s.t $|\mathcal{F}|=\aleph$

Published on 02 Sep 2015 - 8:46

score 1.7k · Answer 11 · 2015-09-03 11:13:22

1.7k

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prove that if X is a countable set of lines in the plane then the union of all lines in X can't cover the plane

Published on 03 Sep 2015 - 11:13

score 318 · Answer 12 · 2015-09-03 13:12:19

318

Views

The cardinality of the integers is divisible by all prime numbers?

Published on 03 Sep 2015 - 13:12

score 258 · Answer 13 · 2026-02-23 10:15:38

258

Views

Total ordering on $\mathcal P(\Bbb R)$

Published on 23 Feb 2026 - 10:15

score 583 · Answer 14 · 2015-09-06 21:19:46

583

Views

Prove: $B=\{x\in \Bbb R\mid x^2\in\Bbb Q\}$ is countable

Published on 06 Sep 2015 - 21:19

score 73 · Answer 15 · 2015-09-07 11:41:21

73

Views

Existence of a partition of a set $X$ which contains at least 2 subsets of $X$ with the same cardinality

Published on 07 Sep 2015 - 11:41

List Question

How to calculate the cardinality of the complement of two countable sets of reals?

Let $\Gamma$ be a $\kappa$-based monotone operator where $\kappa$ is regular. Then the closure ordinal of $\Gamma$ is $\kappa$.

basis for $\mathbb{R}^{\mathbb{N}}:=\left\{f:\mathbb{N}\to\mathbb{R}\right\}$, and its cardinality.

How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?

Characterizing uncountable connected topological spaces

proving $|X|<|Y|$, $|Y|<|Z| \Longrightarrow |X|<|Z|$ without CSB

Give an example of a structure of cardinality $\omega_2$ that has a substructure of $\omega$ but no substructure of $\omega_1$

Does every set have choice sequences as long as the original set?

Prove that the set of all periodic sequences (from some index) of natural numbers is countable

Prove that if $|X|=\aleph _0$ then there exist a family of sets, $\mathcal{F}$, of subsets of $X$, s.t $|\mathcal{F}|=\aleph$

prove that if X is a countable set of lines in the plane then the union of all lines in X can't cover the plane

The cardinality of the integers is divisible by all prime numbers?

Total ordering on $\mathcal P(\Bbb R)$

Prove: $B=\{x\in \Bbb R\mid x^2\in\Bbb Q\}$ is countable

Existence of a partition of a set $X$ which contains at least 2 subsets of $X$ with the same cardinality

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