Question

Proving Cardinality of Cosets in Abstract Algebra

score 108 · Answer 1 · 2026-04-11 10:37:15

108

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Proving Cardinality of Cosets in Abstract Algebra

Published on 11 Apr 2026 - 10:37

score 143 · Answer 2 · 2026-04-10 16:06:09

143

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Prove $\{\alpha\in\mathcal O : |\alpha|\leq \aleph_0\}$ is a set

Published on 10 Apr 2026 - 16:06

score 70 · Answer 3 · 2026-04-14 13:56:02

70

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Let $A$ be a countable set. Prove that $A^{\mathbb N}$ is countable.

Published on 14 Apr 2026 - 13:56

score 484 · Answer 4 · 2026-05-10 17:38:38

484

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Can you lay $ \aleph_1$ many people on a railway track?

Published on 10 May 2026 - 17:38

score 131 · Answer 5 · 2026-04-23 08:04:19

131

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what is the difference between $\aleph_0$ and $ \beth_0$

Published on 23 Apr 2026 - 8:04

score 130 · Answer 6 · 2026-04-18 15:01:32

130

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If an infinite group $G$ acts freely on two sets of same cardinality $> |G|$, then the sets are bijective via an action preserving bijection?

Published on 18 Apr 2026 - 15:01

score 503 · Answer 7 · 2026-04-14 05:36:19

503

Views

What is the cardinality of the set of bounded functions φ:N→N

Published on 14 Apr 2026 - 5:36

score 592 · Answer 8 · 2026-05-10 14:50:23

592

Views

Ordinal vs cardinal dimension

Published on 10 May 2026 - 14:50

score 128 · Answer 9 · 2026-04-15 01:06:39

128

Views

A question regarding a proof pertaining to: for all $n\in\omega$, $(\aleph_{n+1})^{\aleph_0}\leq\aleph_{n+1}\cdot(\aleph_n)^{\aleph_0}$

Published on 15 Apr 2026 - 1:06

score 161 · Answer 10 · 2026-05-10 18:06:12

161

Views

Prove that the power set of $\aleph_0$ =$2^{\aleph_0}$

Published on 10 May 2026 - 18:06

score 150 · Answer 11 · 2026-04-15 17:35:00

150

Views

Set of all functions and showing same cardinality

Published on 15 Apr 2026 - 17:35

score 109 · Answer 12 · 2026-05-10 17:39:37

109

Views

Modifying a sequence of ordinals to be increasing and continuous. (To find names of small rank.)

Published on 10 May 2026 - 17:39

score 113 · Answer 13 · 2026-05-10 16:02:00

113

Views

How best to mathematically describe 'Tristram Shandy problem'

Published on 10 May 2026 - 16:02

score 290 · Answer 14 · 2026-04-15 23:35:53

290

Views

prove that: $|\{x\in\mathbb{\mathbb{R}}:\text{ }\exists r\in S \frac{x}{r}\in\mathbb{N}\}|= |\mathbb{N}|$

Published on 15 Apr 2026 - 23:35

score 110 · Answer 15 · 2026-04-14 10:39:29

110

Views

Successor cardinals independent of ZF

Published on 14 Apr 2026 - 10:39

List Question

Proving Cardinality of Cosets in Abstract Algebra

Prove $\{\alpha\in\mathcal O : |\alpha|\leq \aleph_0\}$ is a set

Let $A$ be a countable set. Prove that $A^{\mathbb N}$ is countable.

Can you lay $ \aleph_1$ many people on a railway track?

what is the difference between $\aleph_0$ and $ \beth_0$

If an infinite group $G$ acts freely on two sets of same cardinality $> |G|$, then the sets are bijective via an action preserving bijection?

What is the cardinality of the set of bounded functions φ:N→N

Ordinal vs cardinal dimension

A question regarding a proof pertaining to: for all $n\in\omega$, $(\aleph_{n+1})^{\aleph_0}\leq\aleph_{n+1}\cdot(\aleph_n)^{\aleph_0}$

Prove that the power set of $\aleph_0$ =$2^{\aleph_0}$

Set of all functions and showing same cardinality

Modifying a sequence of ordinals to be increasing and continuous. (To find names of small rank.)

How best to mathematically describe 'Tristram Shandy problem'

prove that: $|\{x\in\mathbb{\mathbb{R}}:\text{ }\exists r\in S \frac{x}{r}\in\mathbb{N}\}|= |\mathbb{N}|$

Successor cardinals independent of ZF

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