Question

How can I prove (without cardinal numbers) that $P(P(\mathbb{N}))$ is equipollent to $P(P(\mathbb{N})) \times P(P(\mathbb{N}))$

score 143 · Answer 1 · 2021-01-29 21:50:57

143

Views

How can I prove (without cardinal numbers) that $P(P(\mathbb{N}))$ is equipollent to $P(P(\mathbb{N})) \times P(P(\mathbb{N}))$

Published on 29 Jan 2021 - 21:50

score 31 · Answer 2 · 2021-01-30 15:42:39

31

Views

Given two sets $A$ and $B$, is it true that $|B^A|=\max\{|B|,|\mathcal{P}(A)|\}$?

Published on 30 Jan 2021 - 15:42

score 80 · Answer 3 · 2021-01-31 18:31:18

80

Views

If $A\preceq B$ and $C \preceq D$ then $C^A \preceq D^B$

Published on 31 Jan 2021 - 18:31

score 49 · Answer 4 · 2026-04-09 03:46:26

49

Views

bijective function verification

Published on 09 Apr 2026 - 3:46

score 62 · Answer 5 · 2026-04-12 09:51:36

62

Views

Does the definition of cardinal numbers using the equipotent relation require a set of sets?

Published on 12 Apr 2026 - 9:51

score 27 · Answer 6 · 2021-02-04 19:36:51

27

Views

The union of finite subsets $S_k$ of an infinite set $J$ with $k\in K$ with $|K|<|J|$ is strictly smaller than $J$.

Published on 04 Feb 2021 - 19:36

score 98 · Answer 7 · 2026-04-13 02:33:18

98

Views

For any cardinal numbers $a\neq b$, is there a cardinal number $c$ such that $c^a\neq c^b$?

Published on 13 Apr 2026 - 2:33

score 121 · Answer 8 · 2026-04-11 08:44:45

121

Views

Singular power cardinals?

Published on 11 Apr 2026 - 8:44

score 75 · Answer 9 · 2026-04-12 18:47:33

75

Views

Attempt at counting (0,1)

Published on 12 Apr 2026 - 18:47

score 58 · Answer 10 · 2026-04-03 16:27:27

58

Views

uses and proofs of the cardinality of the continuum

Published on 03 Apr 2026 - 16:27

score 86 · Answer 11 · 2021-02-12 07:21:54

86

Views

Does $|\Bbb R^I| = |\Bbb R|$ imply that $I$ is (at most) countable?

Published on 12 Feb 2021 - 7:21

score 94 · Answer 12 · 2026-03-26 17:33:42

94

Views

'Cofinality' and base cardinality of convergent net less than cardinality of index set, implies constant from some index onwards?

Published on 26 Mar 2026 - 17:33

score 64 · Answer 13 · 2021-02-15 21:23:51

64

Views

Bijection between $ A ^ {B \cup C} $ and $ A ^ B \times A ^ C $, with $B\cap C=\varnothing$.

Published on 15 Feb 2021 - 21:23

score 132 · Answer 14 · 2026-04-12 18:11:21

132

Views

Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?

Published on 12 Apr 2026 - 18:11

score 170 · Answer 15 · 2021-02-17 12:43:23

170

Views

Ordinal numbers make no sense to me. Can anyone please explain?

Published on 17 Feb 2021 - 12:43

List Question

How can I prove (without cardinal numbers) that $P(P(\mathbb{N}))$ is equipollent to $P(P(\mathbb{N})) \times P(P(\mathbb{N}))$

Given two sets $A$ and $B$, is it true that $|B^A|=\max\{|B|,|\mathcal{P}(A)|\}$?

If $A\preceq B$ and $C \preceq D$ then $C^A \preceq D^B$

bijective function verification

Does the definition of cardinal numbers using the equipotent relation require a set of sets?

The union of finite subsets $S_k$ of an infinite set $J$ with $k\in K$ with $|K|<|J|$ is strictly smaller than $J$.

For any cardinal numbers $a\neq b$, is there a cardinal number $c$ such that $c^a\neq c^b$?

Singular power cardinals?

Attempt at counting (0,1)

uses and proofs of the cardinality of the continuum

Does $|\Bbb R^I| = |\Bbb R|$ imply that $I$ is (at most) countable?

'Cofinality' and base cardinality of convergent net less than cardinality of index set, implies constant from some index onwards?

Bijection between $ A ^ {B \cup C} $ and $ A ^ B \times A ^ C $, with $B\cap C=\varnothing$.

Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?

Ordinal numbers make no sense to me. Can anyone please explain?

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