Question

How to show that if $P\subseteq Q$ are finite sets, and $\#P=\#Q$, then $P=Q$?

score 96 · Answer 1 · 2015-01-01 14:08:27

96

Views

How to show that if $P\subseteq Q$ are finite sets, and $\#P=\#Q$, then $P=Q$?

Published on 01 Jan 2015 - 14:08

score 212 · Answer 2 · 2026-03-27 16:16:02

212

Views

Prove that $\forall\alpha\geq\omega$, $|L_\alpha|=|\alpha|$ without AC

Published on 27 Mar 2026 - 16:16

score 377 · Answer 3 · 2015-01-02 05:46:44

377

Views

Cardinality of the countably infinite product of a two-point set $\{0,1\}$?

Published on 02 Jan 2015 - 5:46

score 542 · Answer 4 · 2019-10-04 04:48:13

542

Views

Cardinality of power set and binary sequence

Published on 04 Oct 2019 - 4:48

score 91 · Answer 5 · 2019-10-04 07:51:37

91

Views

$\mathcal P(X) \cong \mathcal P(X)$ without singletons if the set $X$ is infinite

Published on 04 Oct 2019 - 7:51

score 359 · Answer 6 · 2019-10-04 22:35:23

359

Views

Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set

Published on 04 Oct 2019 - 22:35

score 42 · Answer 7 · 2019-10-04 22:56:35

42

Views

Countable Union of sets of the same cardinality

Published on 04 Oct 2019 - 22:56

score 171 · Answer 8 · 2019-10-10 00:21:54

171

Views

Cardinality of an arbitrary cartesian product

Published on 10 Oct 2019 - 0:21

score 61 · Answer 9 · 2019-10-10 05:22:12

61

Views

$C$ is a collection of subsets of $\Omega$ of cardinality $|C| = n$. Show that $|\sigma(C)| \leq 2^{2^n}$

Published on 10 Oct 2019 - 5:22

score 407 · Answer 10 · 2019-10-10 15:44:57

407

Views

Cardinality of the following sets

Published on 10 Oct 2019 - 15:44

score 186 · Answer 11 · 2019-10-15 07:34:37

186

Views

Adding 84 inaccessible cardinals to ZFC can be inconsistent if...

Published on 15 Oct 2019 - 7:34

score 122 · Answer 12 · 2026-03-28 16:56:40

122

Views

Uncountable homogeneous linear orders

Published on 28 Mar 2026 - 16:56

score 86 · Answer 13 · 2026-03-27 14:58:43

86

Views

Set theoretical proof about cardinalities of natural numbers

Published on 27 Mar 2026 - 14:58

score 724 · Answer 14 · 2019-10-20 14:48:18

724

Views

Functions mapping natural numbers to {0, 1} has same cardinality as functions mapping natural numbers to natural numbers

Published on 20 Oct 2019 - 14:48

score 784 · Answer 15 · 2019-10-21 09:26:08

784

Views

Uncountably many functions coinciding only finitely many values

Published on 21 Oct 2019 - 9:26

List Question

How to show that if $P\subseteq Q$ are finite sets, and $\#P=\#Q$, then $P=Q$?

Prove that $\forall\alpha\geq\omega$, $|L_\alpha|=|\alpha|$ without AC

Cardinality of the countably infinite product of a two-point set $\{0,1\}$?

Cardinality of power set and binary sequence

$\mathcal P(X) \cong \mathcal P(X)$ without singletons if the set $X$ is infinite

Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set

Countable Union of sets of the same cardinality

Cardinality of an arbitrary cartesian product

$C$ is a collection of subsets of $\Omega$ of cardinality $|C| = n$. Show that $|\sigma(C)| \leq 2^{2^n}$

Cardinality of the following sets

Adding 84 inaccessible cardinals to ZFC can be inconsistent if...

Uncountable homogeneous linear orders

Set theoretical proof about cardinalities of natural numbers

Functions mapping natural numbers to {0, 1} has same cardinality as functions mapping natural numbers to natural numbers

Uncountably many functions coinciding only finitely many values

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