Question

Non-existence of a surjection

score 83 · Answer 1 · 2023-07-02 17:40:35

83

Views

Non-existence of a surjection

Published on 02 Jul 2023 - 17:40

score 93 · Answer 2 · 2023-07-04 15:13:07

93

Views

Proving countability and uncountability

Published on 04 Jul 2023 - 15:13

score 85 · Answer 3 · 2023-07-06 00:18:38

85

Views

Classification of Open Subsets of $\mathbb{R}^2$

Published on 06 Jul 2023 - 0:18

score 92 · Answer 4 · 2026-03-29 09:10:11

92

Views

Non-isomorphic well-orderings on a set

Published on 29 Mar 2026 - 9:10

score 140 · Answer 5 · 2023-07-07 23:49:41

140

Views

Intuition About the Infinite Monkey Theorem

Published on 07 Jul 2023 - 23:49

score 757 · Answer 6 · 2026-03-30 08:32:38

757

Views

Why isn't the $\aleph$-fixed-point the largest cardinal number?

Published on 30 Mar 2026 - 8:32

score 53 · Answer 7 · 2023-07-09 03:17:57

53

Views

Cardinality of $A = \{E \subseteq \mathbb{N}: \exists p \text{ prime},n \in \mathbb{N} \text{ such that }|E| = p^n\}$

Published on 09 Jul 2023 - 3:17

score 23 · Answer 8 · 2023-07-09 06:44:47

23

Views

In cardinal arithmetic does $\alpha ^\beta = \alpha$ for $\beta $ much smaller than $\alpha$?

Published on 09 Jul 2023 - 6:44

score 81 · Answer 9 · 2026-03-29 09:10:08

81

Views

Proving directly that $\aleph_{\alpha+1} \cdot \aleph_{\alpha+1} = \aleph_{\alpha+1}$ by recursion

Published on 29 Mar 2026 - 9:10

score 68 · Answer 10 · 2023-07-10 09:36:36

68

Views

$\sum_{i\in I} \kappa_i \leq \prod_{i\in I} \lambda_i $ when $\kappa_i < \lambda_i$ for all $i\in I$ and $\kappa_i,\lambda_i$ are cardinals.

Published on 10 Jul 2023 - 9:36

score 30 · Answer 11 · 2023-07-12 16:21:37

30

Views

Uncountable union of chain of subsets of R

Published on 12 Jul 2023 - 16:21

score 323 · Answer 12 · 2023-07-14 11:29:34

323

Views

Struggling to Prove Cantor's Theorem (textbook guided exercise)

Published on 14 Jul 2023 - 11:29

score 106 · Answer 13 · 2023-07-16 22:48:51

106

Views

Easy accessible proof that $ |\mathcal{P} (\mathbb{N}) | = |\mathbb{R}|$?

Published on 16 Jul 2023 - 22:48

score 59 · Answer 14 · 2023-07-21 11:15:03

59

Views

Given |A\B| = |B\A|, prove |A|=|B| and provide 2 sets (A and B) such that |A| = |B| but |A\B| is not the same as |B\A|

Published on 21 Jul 2023 - 11:15

score 56 · Answer 15 · 2023-07-22 11:54:28

56

Views

Proving proper inequality of cardinality of sets is transitive

Published on 22 Jul 2023 - 11:54

List Question

Non-existence of a surjection

Proving countability and uncountability

Classification of Open Subsets of $\mathbb{R}^2$

Non-isomorphic well-orderings on a set

Intuition About the Infinite Monkey Theorem

Why isn't the $\aleph$-fixed-point the largest cardinal number?

Cardinality of $A = \{E \subseteq \mathbb{N}: \exists p \text{ prime},n \in \mathbb{N} \text{ such that }|E| = p^n\}$

In cardinal arithmetic does $\alpha ^\beta = \alpha$ for $\beta $ much smaller than $\alpha$?

Proving directly that $\aleph_{\alpha+1} \cdot \aleph_{\alpha+1} = \aleph_{\alpha+1}$ by recursion

$\sum_{i\in I} \kappa_i \leq \prod_{i\in I} \lambda_i $ when $\kappa_i < \lambda_i$ for all $i\in I$ and $\kappa_i,\lambda_i$ are cardinals.

Uncountable union of chain of subsets of R

Struggling to Prove Cantor's Theorem (textbook guided exercise)

Easy accessible proof that $ |\mathcal{P} (\mathbb{N}) | = |\mathbb{R}|$?

Given |A\B| = |B\A|, prove |A|=|B| and provide 2 sets (A and B) such that |A| = |B| but |A\B| is not the same as |B\A|

Proving proper inequality of cardinality of sets is transitive

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