Question

Cardinality of the set of all infinite monotonically decreasing sequences of naturals

score 777 · Answer 1 · 2016-06-26 08:50:07

777

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Cardinality of the set of all infinite monotonically decreasing sequences of naturals

Published on 26 Jun 2016 - 8:50

score 115 · Answer 2 · 2016-06-29 04:33:30

115

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Let $R$ be an infinite comutative ring with unity, $M,N$ be $R$-modules, $f:M \to N$ be a surjective module homomorphism; then $|M|=|N ||\ker f|$?

Published on 29 Jun 2016 - 4:33

score 167 · Answer 3 · 2016-06-30 03:17:45

167

Views

Counting subsets of different sizes of a set

Published on 30 Jun 2016 - 3:17

score 604 · Answer 4 · 2013-04-01 00:54:06

604

Views

Proving that if $A$ is a non-empty set, then $|A| ≤ |A \times A|$

Published on 01 Apr 2013 - 0:54

score 2k · Answer 5 · 2013-04-01 01:52:08

2k

Views

If A is a denumerable set, and there exists a surjective function from A to B, then B is denumerable

Published on 01 Apr 2013 - 1:52

score 687 · Answer 6 · 2026-04-04 01:53:17

687

Views

How to prove that a regular cardinal cannot be expressed as a union of sets with less cardinality?

Published on 04 Apr 2026 - 1:53

score 74 · Answer 7 · 2013-04-01 13:05:05

74

Views

CCC and point separating weight

Published on 01 Apr 2013 - 13:05

score 68 · Answer 8 · 2013-04-03 03:24:02

68

Views

X ≼ Y ≼ Z and |X| = |Z|. Prove |Y|=|Z|.

Published on 03 Apr 2013 - 3:24

score 1.6k · Answer 9 · 2013-04-04 02:11:09

1.6k

Views

The class of cardinal numbers is well ordered

Published on 04 Apr 2013 - 2:11

score 1.2k · Answer 10 · 2013-04-04 06:01:16

1.2k

Views

cardinality of the set of $ \varphi: \mathbb N \to \mathbb N$ such that $\varphi$ is an increasing sequence

Published on 04 Apr 2013 - 6:01

score 785 · Answer 11 · 2013-04-04 09:59:56

785

Views

Looking for a problem where one could use a cardinality argument to find a solution.

Published on 04 Apr 2013 - 9:59

score 129 · Answer 12 · 2013-04-04 13:31:04

129

Views

GCH implies that $2^{<\kappa}=\kappa$

Published on 04 Apr 2013 - 13:31

score 72 · Answer 13 · 2013-04-05 07:37:04

72

Views

length of a normal not cofinal sequence

Published on 05 Apr 2013 - 7:37

score 3.1k · Answer 14 · 2013-04-05 18:24:46

3.1k

Views

Bijection between $\mathbb R^\mathbb N$ and $\mathbb R$

Published on 05 Apr 2013 - 18:24

score 123 · Answer 15 · 2026-04-02 17:05:20

123

Views

How to show this space $X$ is countably compact, first countable?

Published on 02 Apr 2026 - 17:05

List Question

Cardinality of the set of all infinite monotonically decreasing sequences of naturals

Let $R$ be an infinite comutative ring with unity, $M,N$ be $R$-modules, $f:M \to N$ be a surjective module homomorphism; then $|M|=|N ||\ker f|$?

Counting subsets of different sizes of a set

Proving that if $A$ is a non-empty set, then $|A| ≤ |A \times A|$

If A is a denumerable set, and there exists a surjective function from A to B, then B is denumerable

How to prove that a regular cardinal cannot be expressed as a union of sets with less cardinality?

CCC and point separating weight

X ≼ Y ≼ Z and |X| = |Z|. Prove |Y|=|Z|.

The class of cardinal numbers is well ordered

cardinality of the set of $ \varphi: \mathbb N \to \mathbb N$ such that $\varphi$ is an increasing sequence

Looking for a problem where one could use a cardinality argument to find a solution.

GCH implies that $2^{<\kappa}=\kappa$

length of a normal not cofinal sequence

Bijection between $\mathbb R^\mathbb N$ and $\mathbb R$

How to show this space $X$ is countably compact, first countable?

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