Question

An alternative succinct proof needed for trivial cardinality fact

score 67 · Answer 1 · 2026-03-27 02:59:48

67

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An alternative succinct proof needed for trivial cardinality fact

Published on 27 Mar 2026 - 2:59

score 448 · Answer 2 · 2014-04-12 03:57:28

448

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Proving that $\mathrm{card}(2^{\mathbb{N}})=\mathrm{card}(\mathbb{N}^\mathbb{N})$

Published on 12 Apr 2014 - 3:57

score 3k · Answer 3 · 2014-04-14 23:11:38

3k

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Cardinality of two sets cross-multiplied

Published on 14 Apr 2014 - 23:11

score 132 · Answer 4 · 2014-04-16 05:00:42

132

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If $X$ is a finite set of cardinality $n$, where $n$ exists in $P$, show that the following conditions on a function $f: X \to X$ are equivalent:

Published on 16 Apr 2014 - 5:00

score 173 · Answer 5 · 2014-04-16 09:13:35

173

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Cardinality of $\lim_{k\to\infty}\mathbb N^k$ vs. $\mathbb N^\infty$

Published on 16 Apr 2014 - 9:13

score 77 · Answer 6 · 2014-04-16 17:57:56

77

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cardinality with finite sets

Published on 16 Apr 2014 - 17:57

score 3.3k · Answer 7 · 2014-04-16 23:00:42

3.3k

Views

Proving that (0,1) and [0,1] are numerically equivalent.

Published on 16 Apr 2014 - 23:00

score 476 · Answer 8 · 2014-04-17 00:23:44

476

Views

Prove that $\{(a,b):a,b\in\mathbb N, a\geq b\}$ is denumerable.

Published on 17 Apr 2014 - 0:23

score 128 · Answer 9 · 2014-04-18 03:48:09

128

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How many ways can we totally order a set $X$ (but not necessarily the whole set $X$, perhaps just a subset) up to isomorphism?

Published on 18 Apr 2014 - 3:48

score 145 · Answer 10 · 2026-03-25 19:01:51

145

Views

Preserve Cardinals and Adding No Bounded Subsets

Published on 25 Mar 2026 - 19:01

score 199 · Answer 11 · 2014-04-21 15:14:21

199

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Cardinality of the set of all involutions from $\mathbb N$ to itself

Published on 21 Apr 2014 - 15:14

score 2.7k · Answer 12 · 2026-03-27 13:42:18

2.7k

Views

Cardinality of the set of at most countable subsets of the real line?

Published on 27 Mar 2026 - 13:42

score 303 · Answer 13 · 2014-04-21 22:56:48

303

Views

Determining the cardinality of these sets.

Published on 21 Apr 2014 - 22:56

score 414 · Answer 14 · 2014-04-22 11:15:04

414

Views

How can we show that $\omega_1$ is a regular cardinal?

Published on 22 Apr 2014 - 11:15

score 171 · Answer 15 · 2014-04-23 07:05:24

171

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Do we need choice to prove that $|\mathbb{N} \times A| = |A|$ for all infinite sets $A$?

Published on 23 Apr 2014 - 7:05

List Question

An alternative succinct proof needed for trivial cardinality fact

Proving that $\mathrm{card}(2^{\mathbb{N}})=\mathrm{card}(\mathbb{N}^\mathbb{N})$

Cardinality of two sets cross-multiplied

If $X$ is a finite set of cardinality $n$, where $n$ exists in $P$, show that the following conditions on a function $f: X \to X$ are equivalent:

Cardinality of $\lim_{k\to\infty}\mathbb N^k$ vs. $\mathbb N^\infty$

cardinality with finite sets

Proving that (0,1) and [0,1] are numerically equivalent.

Prove that $\{(a,b):a,b\in\mathbb N, a\geq b\}$ is denumerable.

How many ways can we totally order a set $X$ (but not necessarily the whole set $X$, perhaps just a subset) up to isomorphism?

Preserve Cardinals and Adding No Bounded Subsets

Cardinality of the set of all involutions from $\mathbb N$ to itself

Cardinality of the set of at most countable subsets of the real line?

Determining the cardinality of these sets.

How can we show that $\omega_1$ is a regular cardinal?

Do we need choice to prove that $|\mathbb{N} \times A| = |A|$ for all infinite sets $A$?

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