Question

$A$ infinite implies $|A|=|A|^n$ for any $n\in \mathbb{N}$

score 107 · Answer 1 · 2017-09-21 01:16:48

107

Views

$A$ infinite implies $|A|=|A|^n$ for any $n\in \mathbb{N}$

Published on 21 Sep 2017 - 1:16

score 156 · Answer 2 · 2017-09-21 10:44:37

156

Views

What is the smallest $i$ such that ZFC proves $\mathfrak c\le \aleph_i$?

Published on 21 Sep 2017 - 10:44

score 108 · Answer 3 · 2026-04-05 19:06:36

108

Views

Cardinality of set of finite subsets of $A$ equals cardinality of $A$

Published on 05 Apr 2026 - 19:06

score 241 · Answer 4 · 2026-03-25 12:55:29

241

Views

Two infinite bases for a vector space have equal cardinality

Published on 25 Mar 2026 - 12:55

score 38 · Answer 5 · 2017-09-22 16:04:07

38

Views

For $A$ an infinite set, and $f: A^A \to A$, does there exist $a\in A$ such that $f^{-1}(\{a\}) \cong A^A$?

Published on 22 Sep 2017 - 16:04

score 120 · Answer 6 · 2017-09-23 03:30:39

120

Views

How many equivalence classes are there in this closeness relation on sequences?

Published on 23 Sep 2017 - 3:30

score 176 · Answer 7 · 2017-09-24 19:47:38

176

Views

Is the cardinal $2^{\aleph_0}$ regular, working in ZFC?

Published on 24 Sep 2017 - 19:47

score 75 · Answer 8 · 2026-04-01 12:12:33

75

Views

Cofinality as an axiom?

Published on 01 Apr 2026 - 12:12

score 71 · Answer 9 · 2017-09-25 06:56:38

71

Views

Prove $ |A \cup B| = |[0,1]| \Rightarrow |A|=|[0,1]| \bigvee |B|=|[0,1]| $

Published on 25 Sep 2017 - 6:56

score 842 · Answer 10 · 2026-04-06 17:24:44

842

Views

How is raising 2 to the power of a cardinality equivalent to taking the power set?

Published on 06 Apr 2026 - 17:24

score 6.4k · Answer 11 · 2026-03-30 08:30:10

6.4k

Views

Doesn't the unprovability of the continuum hypothesis prove the continuum hypothesis?

Published on 30 Mar 2026 - 8:30

score 127 · Answer 12 · 2026-04-06 12:59:21

127

Views

How to prove the uncountability of reals by using "describability"?

Published on 06 Apr 2026 - 12:59

score 666 · Answer 13 · 2026-04-06 17:26:15

666

Views

If $A$ is infinite set, then there is a subset $B$ of $A$ such that $|A|=|B|=|A-B|$

Published on 06 Apr 2026 - 17:26

score 94 · Answer 14 · 2026-04-05 20:54:14

94

Views

Questions on the use of axiom of choice

Published on 05 Apr 2026 - 20:54

score 537 · Answer 15 · 2017-10-01 03:46:53

537

Views

A theory with only countably many non-isomorphic countable models can be completed

Published on 01 Oct 2017 - 3:46

List Question

$A$ infinite implies $|A|=|A|^n$ for any $n\in \mathbb{N}$

What is the smallest $i$ such that ZFC proves $\mathfrak c\le \aleph_i$?

Cardinality of set of finite subsets of $A$ equals cardinality of $A$

Two infinite bases for a vector space have equal cardinality

For $A$ an infinite set, and $f: A^A \to A$, does there exist $a\in A$ such that $f^{-1}(\{a\}) \cong A^A$?

How many equivalence classes are there in this closeness relation on sequences?

Is the cardinal $2^{\aleph_0}$ regular, working in ZFC?

Cofinality as an axiom?

Prove $ |A \cup B| = |[0,1]| \Rightarrow |A|=|[0,1]| \bigvee |B|=|[0,1]| $

How is raising 2 to the power of a cardinality equivalent to taking the power set?

Doesn't the unprovability of the continuum hypothesis prove the continuum hypothesis?

How to prove the uncountability of reals by using "describability"?

If $A$ is infinite set, then there is a subset $B$ of $A$ such that $|A|=|B|=|A-B|$

Questions on the use of axiom of choice

A theory with only countably many non-isomorphic countable models can be completed

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