Question

Set cardinality, function onto, open unit square maps into real number set

score 2.4k · Answer 1 · 2015-02-26 03:22:16

2.4k

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Set cardinality, function onto, open unit square maps into real number set

Published on 26 Feb 2015 - 3:22

score 82 · Answer 2 · 2015-02-26 14:17:23

82

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$\operatorname{Card}(X) \leq\operatorname{Card}(Y)$ iff $\aleph (X) \leq \aleph(Y)$

Published on 26 Feb 2015 - 14:17

score 448 · Answer 3 · 2015-03-03 11:26:30

448

Views

Halmos' Naive Set Theory Cardinal Arithmetic Exercise

Published on 03 Mar 2015 - 11:26

score 882 · Answer 4 · 2015-03-05 13:29:03

882

Views

Enderton's Elements of Set Theory Scott's Trick Exercise (page 207 problem 31)

Published on 05 Mar 2015 - 13:29

score 1.3k · Answer 5 · 2026-03-26 12:35:50

1.3k

Views

Let $V,W$ be two countably infinite dimensional vector space over the same field , then are $V,W$ isomorphic as vector spaces?

Published on 26 Mar 2026 - 12:35

score 104 · Answer 6 · 2026-03-30 22:01:39

104

Views

Does $\lambda^2 \leq \kappa^2 \Rightarrow \lambda \leq \kappa$ imply the axiom of choice?

Published on 30 Mar 2026 - 22:01

score 27 · Answer 7 · 2015-03-06 15:16:14

27

Views

Let $A$ be any non-empty set and $\alpha$ be an infinite cardinal . When can we say $|A^\alpha|=\alpha$ ?

Published on 06 Mar 2015 - 15:16

score 66 · Answer 8 · 2015-03-07 17:35:23

66

Views

Clarification on the proof of Theorem 8. 11 (Hungerford)

Published on 07 Mar 2015 - 17:35

score 61 · Answer 9 · 2026-04-02 16:00:15

61

Views

Question related to ordinal number without using Axiom of Choice.

Published on 02 Apr 2026 - 16:00

score 1.4k · Answer 10 · 2015-03-09 03:54:51

1.4k

Views

Countable union of sets of cardinality $c$ has cardinality $c$

Published on 09 Mar 2015 - 3:54

score 89 · Answer 11 · 2026-03-29 03:45:17

89

Views

Replacing an ordinal with its cardinality in a partition relation

Published on 29 Mar 2026 - 3:45

score 321 · Answer 12 · 2015-03-11 02:27:45

321

Views

For each ordinal $\alpha$, $\alpha\le \aleph_{\alpha}$

Published on 11 Mar 2015 - 2:27

score 255 · Answer 13 · 2015-03-11 13:04:50

255

Views

Finite sum over uncountable set

Published on 11 Mar 2015 - 13:04

score 401 · Answer 14 · 2015-03-12 11:07:23

401

Views

On the cardinality of $\mathbb R \times ...\aleph_1 {times}$ and $\mathbb R \times ...2^{\aleph_0} \space {times}$

Published on 12 Mar 2015 - 11:07

score 82 · Answer 15 · 2015-03-12 17:48:53

82

Views

Let $A, |A|=a$ be a set where $a$ is infinite. How many equivalence relations are there over $A$?

Published on 12 Mar 2015 - 17:48

List Question

Set cardinality, function onto, open unit square maps into real number set

$\operatorname{Card}(X) \leq\operatorname{Card}(Y)$ iff $\aleph (X) \leq \aleph(Y)$

Halmos' Naive Set Theory Cardinal Arithmetic Exercise

Enderton's Elements of Set Theory Scott's Trick Exercise (page 207 problem 31)

Let $V,W$ be two countably infinite dimensional vector space over the same field , then are $V,W$ isomorphic as vector spaces?

Does $\lambda^2 \leq \kappa^2 \Rightarrow \lambda \leq \kappa$ imply the axiom of choice?

Let $A$ be any non-empty set and $\alpha$ be an infinite cardinal . When can we say $|A^\alpha|=\alpha$ ?

Clarification on the proof of Theorem 8. 11 (Hungerford)

Question related to ordinal number without using Axiom of Choice.

Countable union of sets of cardinality $c$ has cardinality $c$

Replacing an ordinal with its cardinality in a partition relation

For each ordinal $\alpha$, $\alpha\le \aleph_{\alpha}$

Finite sum over uncountable set

On the cardinality of $\mathbb R \times ...\aleph_1 {times}$ and $\mathbb R \times ...2^{\aleph_0} \space {times}$

Let $A, |A|=a$ be a set where $a$ is infinite. How many equivalence relations are there over $A$?

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