Question

How do we show if $|A|\le|B|$ then $|B|\not\lt|A|$ using Cantor-Schröder-Bernstein Theorem?

score 106 · Answer 1 · 2026-04-13 06:55:58

106

Views

How do we show if $|A|\le|B|$ then $|B|\not\lt|A|$ using Cantor-Schröder-Bernstein Theorem?

Published on 13 Apr 2026 - 6:55

score 111 · Answer 2 · 2026-04-13 08:04:06

111

Views

Proof of $\mathcal{F}\approx\mathcal{P}(\mathbb{N})$ using elementary notations and Cantor Bernstein Theorem?

Published on 13 Apr 2026 - 8:04

score 91 · Answer 3 · 2026-03-31 12:14:29

91

Views

Is there any use to $\mathbb{N}$ as a sort of ring mod an infinite number?

Published on 31 Mar 2026 - 12:14

score 199 · Answer 4 · 2021-05-01 00:40:32

199

Views

If $\lambda$ is a limit cardinal then $\kappa^\lambda = (\kappa^{<\lambda})^{cf \lambda}$ for each cardinal $\kappa$.

Published on 01 May 2021 - 0:40

score 52 · Answer 5 · 2021-05-02 13:08:44

52

Views

Prove that : $|P(\mathbb{R}) \setminus P(\mathbb{R}\setminus \mathbb{Z})| = 2^{2^{\aleph_0}}$

Published on 02 May 2021 - 13:08

score 104 · Answer 6 · 2026-03-28 06:17:44

104

Views

Linear ordering and cardinal numbers - Problem 5.3 Jech's book

Published on 28 Mar 2026 - 6:17

score 157 · Answer 7 · 2021-05-04 18:55:06

157

Views

Cardinal arithmetic- Problem 5.18 Jech's book

Published on 04 May 2021 - 18:55

score 61 · Answer 8 · 2026-04-10 06:25:03

61

Views

Cardinality of continuous functions

Published on 10 Apr 2026 - 6:25

score 85 · Answer 9 · 2026-04-13 10:02:08

85

Views

Given two sets having the same cardinality what can we say about the cardinality when they are subtracted from another set

Published on 13 Apr 2026 - 10:02

score 21 · Answer 10 · 2026-04-13 11:02:51

21

Views

How do you the use regularity of this cardinal in the result?

Published on 13 Apr 2026 - 11:02

score 89 · Answer 11 · 2021-05-09 13:10:04

89

Views

$ [0,1] \cup \mathbb{N} \sim [0,1] $

Published on 09 May 2021 - 13:10

score 99 · Answer 12 · 2021-05-10 05:57:29

99

Views

Why does $|\mathfrak N| = c$ imply $|\mathfrak M| = 2^c$? (Proof of uncountability of infinite $\sigma$-algebras)

Published on 10 May 2021 - 5:57

score 57 · Answer 13 · 2026-04-12 17:38:31

57

Views

Thinking about continuous functions as vectors with continuum-many components.

Published on 12 Apr 2026 - 17:38

score 43 · Answer 14 · 2021-05-13 22:20:05

43

Views

bijective and injective maps

Published on 13 May 2021 - 22:20

score 48 · Answer 15 · 2026-04-12 07:15:13

48

Views

cardinality of specific sets without using cardinal arithmetic

Published on 12 Apr 2026 - 7:15

List Question

How do we show if $|A|\le|B|$ then $|B|\not\lt|A|$ using Cantor-Schröder-Bernstein Theorem?

Proof of $\mathcal{F}\approx\mathcal{P}(\mathbb{N})$ using elementary notations and Cantor Bernstein Theorem?

Is there any use to $\mathbb{N}$ as a sort of ring mod an infinite number?

If $\lambda$ is a limit cardinal then $\kappa^\lambda = (\kappa^{<\lambda})^{cf \lambda}$ for each cardinal $\kappa$.

Prove that : $|P(\mathbb{R}) \setminus P(\mathbb{R}\setminus \mathbb{Z})| = 2^{2^{\aleph_0}}$

Linear ordering and cardinal numbers - Problem 5.3 Jech's book

Cardinal arithmetic- Problem 5.18 Jech's book

Cardinality of continuous functions

Given two sets having the same cardinality what can we say about the cardinality when they are subtracted from another set

How do you the use regularity of this cardinal in the result?

$ [0,1] \cup \mathbb{N} \sim [0,1] $

Why does $|\mathfrak N| = c$ imply $|\mathfrak M| = 2^c$? (Proof of uncountability of infinite $\sigma$-algebras)

Thinking about continuous functions as vectors with continuum-many components.

bijective and injective maps

cardinality of specific sets without using cardinal arithmetic

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