Question

Show that $\operatorname{cf}(2^{<\kappa})\geq\operatorname{cf}(\kappa)$

score 56 · Answer 1 · 2026-03-29 07:29:15

56

Views

Show that $\operatorname{cf}(2^{<\kappa})\geq\operatorname{cf}(\kappa)$

Published on 29 Mar 2026 - 7:29

score 98 · Answer 2 · 2026-03-29 07:19:47

98

Views

Successor of a regular cardinal does not reflect stationary sets

Published on 29 Mar 2026 - 7:19

score 89 · Answer 3 · 2023-05-09 18:29:57

89

Views

Compare cardinality of two sets

Published on 09 May 2023 - 18:29

score 955 · Answer 4 · 2026-03-30 11:22:40

955

Views

Formal Definition of Cardinality

Published on 30 Mar 2026 - 11:22

score 72 · Answer 5 · 2023-05-15 17:33:18

72

Views

Any partition of an at most countable set has a set of representatives.

Published on 15 May 2023 - 17:33

score 59 · Answer 6 · 2026-03-29 04:34:33

59

Views

Examples of existence proof by comparison of cardinalities

Published on 29 Mar 2026 - 4:34

score 85 · Answer 7 · 2023-05-17 18:01:12

85

Views

Cofinality condition for union of sets with lower cardinality

Published on 17 May 2023 - 18:01

score 59 · Answer 8 · 2023-05-18 12:52:33

59

Views

If $X$ and $Y$ are equipotent then the bijections set of $X$ into $X$ is equipotent to the bijections set of $Y$ into $Y$.

Published on 18 May 2023 - 12:52

score 80 · Answer 9 · 2026-03-28 02:10:35

80

Views

Are there any applied mathematics problems which require a set with cardinality greater than the Reals?

Published on 28 Mar 2026 - 2:10

score 75 · Answer 10 · 2023-05-20 13:20:21

75

Views

Let $L$ be a (topological) complement of $G$. Is $\dim G = \operatorname{codim} L$?

Published on 20 May 2023 - 13:20

score 52 · Answer 11 · 2023-05-20 16:43:17

52

Views

Let $A$ be countable. The set $[A]^n:=\{S \subseteq A|| S \mid=n\}$ is countable for all $n \in N, n \neq 0$

Published on 20 May 2023 - 16:43

score 110 · Answer 12 · 2023-05-23 20:31:10

110

Views

What is the cardinality of $A \times \mathbb N$ if $\left \lvert A \right \rvert \geq \aleph_0\ $?

Published on 23 May 2023 - 20:31

score 83 · Answer 13 · 2023-05-24 22:48:10

83

Views

$\bigcup_{n=0}^{\infty} A_n$ is at most countable

Published on 24 May 2023 - 22:48

score 88 · Answer 14 · 2023-05-29 16:50:40

88

Views

Associativity of cardinal multiplication

Published on 29 May 2023 - 16:50

score 181 · Answer 15 · 2026-03-30 16:26:36

181

Views

Is it true that $\aleph_1=2^{\aleph_0}$, and if so, would the limit of $2^x$ as $x$ approaches $+\infty$ be equal to $\aleph_1$?

Published on 30 Mar 2026 - 16:26

List Question

Show that $\operatorname{cf}(2^{<\kappa})\geq\operatorname{cf}(\kappa)$

Successor of a regular cardinal does not reflect stationary sets

Compare cardinality of two sets

Formal Definition of Cardinality

Any partition of an at most countable set has a set of representatives.

Examples of existence proof by comparison of cardinalities

Cofinality condition for union of sets with lower cardinality

If $X$ and $Y$ are equipotent then the bijections set of $X$ into $X$ is equipotent to the bijections set of $Y$ into $Y$.

Are there any applied mathematics problems which require a set with cardinality greater than the Reals?

Let $L$ be a (topological) complement of $G$. Is $\dim G = \operatorname{codim} L$?

Let $A$ be countable. The set $[A]^n:=\{S \subseteq A|| S \mid=n\}$ is countable for all $n \in N, n \neq 0$

What is the cardinality of $A \times \mathbb N$ if $\left \lvert A \right \rvert \geq \aleph_0\ $?

$\bigcup_{n=0}^{\infty} A_n$ is at most countable

Associativity of cardinal multiplication

Is it true that $\aleph_1=2^{\aleph_0}$, and if so, would the limit of $2^x$ as $x$ approaches $+\infty$ be equal to $\aleph_1$?

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