Question

Cardinality and Bijections- Proof Problem

score 1k · Answer 1 · 2019-11-26 05:23:46

1k

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Cardinality and Bijections- Proof Problem

Published on 26 Nov 2019 - 5:23

score 963 · Answer 2 · 2019-11-26 05:39:27

963

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Proving that the cardinality of the set of all bijective functions from $\mathbb N$ to $\mathbb N$ is $c$

Published on 26 Nov 2019 - 5:39

score 66 · Answer 3 · 2026-03-27 18:08:15

66

Views

How do I prove that $|\Bbb N^\Bbb N|$ is equal to $|2^\Bbb N|$?

Published on 27 Mar 2026 - 18:08

score 84 · Answer 4 · 2019-11-27 20:22:58

84

Views

Are there an uncountable subset of $\mathcal{P}(\mathbb{N})$ such that it has total order under the subset relation?

Published on 27 Nov 2019 - 20:22

score 70 · Answer 5 · 2019-11-28 17:39:29

70

Views

Countability with Infinite Sets- Proofs Question

Published on 28 Nov 2019 - 17:39

score 67 · Answer 6 · 2019-11-29 05:54:29

67

Views

Equality of Cardinality of Cartesian Sets

Published on 29 Nov 2019 - 5:54

score 22 · Answer 7 · 2019-11-29 16:00:47

22

Views

Equality of Cardinality of a Power Set to a Set of Functions

Published on 29 Nov 2019 - 16:00

score 97 · Answer 8 · 2019-11-29 19:41:39

97

Views

Cantor's Diagonalization Argument- Application Proof Problem

Published on 29 Nov 2019 - 19:41

score 108 · Answer 9 · 2019-12-01 13:11:37

108

Views

What is the probability that a random function $\kappa\times\lambda\rightarrow\{0,1\}$ is constant in $y$ for some $x$?

Published on 01 Dec 2019 - 13:11

score 71 · Answer 10 · 2019-12-01 18:38:08

71

Views

Dense subsets of ${}^{<\kappa} \kappa$, with $\kappa$ regular cardinal

Published on 01 Dec 2019 - 18:38

score 21 · Answer 11 · 2019-12-04 13:21:50

21

Views

Cardinality: Equality between |P(A)^B| and |P(B)^A|.

Published on 04 Dec 2019 - 13:21

score 72 · Answer 12 · 2026-03-27 19:33:39

72

Views

Construction a club $C\subseteq\omega_1$ and a scale of length $\aleph_{\omega_1+1}$ in $\prod_{\alpha \in C}\aleph_{\alpha+1}/J$

Published on 27 Mar 2026 - 19:33

score 114 · Answer 13 · 2019-12-10 08:58:32

114

Views

cardinal number arithmetic regarding exponentiation

Published on 10 Dec 2019 - 8:58

score 76 · Answer 14 · 2026-03-27 19:30:08

76

Views

exact upper bound

Published on 27 Mar 2026 - 19:30

score 120 · Answer 15 · 2019-12-11 22:31:38

120

Views

Does there exist an injection $\mathbb{R} \to\mathbb{N} \times \mathbb{ Z} \times \mathbb{ Q}$?

Published on 11 Dec 2019 - 22:31

List Question

Cardinality and Bijections- Proof Problem

Proving that the cardinality of the set of all bijective functions from $\mathbb N$ to $\mathbb N$ is $c$

How do I prove that $|\Bbb N^\Bbb N|$ is equal to $|2^\Bbb N|$?

Are there an uncountable subset of $\mathcal{P}(\mathbb{N})$ such that it has total order under the subset relation?

Countability with Infinite Sets- Proofs Question

Equality of Cardinality of Cartesian Sets

Equality of Cardinality of a Power Set to a Set of Functions

Cantor's Diagonalization Argument- Application Proof Problem

What is the probability that a random function $\kappa\times\lambda\rightarrow\{0,1\}$ is constant in $y$ for some $x$?

Dense subsets of ${}^{<\kappa} \kappa$, with $\kappa$ regular cardinal

Cardinality: Equality between |P(A)^B| and |P(B)^A|.

Construction a club $C\subseteq\omega_1$ and a scale of length $\aleph_{\omega_1+1}$ in $\prod_{\alpha \in C}\aleph_{\alpha+1}/J$

cardinal number arithmetic regarding exponentiation

exact upper bound

Does there exist an injection $\mathbb{R} \to\mathbb{N} \times \mathbb{ Z} \times \mathbb{ Q}$?

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