Question

About Cardinal Exponentiation

score 104 · Answer 1 · 2026-03-28 04:00:52

104

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About Cardinal Exponentiation

Published on 28 Mar 2026 - 4:00

score 156 · Answer 2 · 2020-04-23 10:20:00

156

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If $x$ is a set of cardinality $\kappa$ and $\lambda<\kappa$, do we need the axiom of choice to prove that there is a subset of $x$ of size $\lambda$?

Published on 23 Apr 2020 - 10:20

score 49 · Answer 3 · 2020-04-23 21:51:37

49

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Let $A\subseteq\mathbb{R}$ with $|A|=\omega_1$. Prove $A$ does not embed into $\mathbb{Q}\times\omega_1$.

Published on 23 Apr 2020 - 21:51

score 49 · Answer 4 · 2020-04-24 01:46:14

49

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Let $X\subseteq\mathbb{R}$, and $\forall x\in X, \{y\in X:y>x\}$ is countable. Prove $X$ is countable.

Published on 24 Apr 2020 - 1:46

score 224 · Answer 5 · 2020-04-24 14:20:45

224

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Cardinalities of $\mathbb{R}[X]$ and $\mathbb{R}$

Published on 24 Apr 2020 - 14:20

score 109 · Answer 6 · 2020-04-26 13:11:17

109

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Countable Subset of rational numbers

Published on 26 Apr 2020 - 13:11

score 111 · Answer 7 · 2020-04-26 16:03:05

111

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Continuity of cardinal power function

Published on 26 Apr 2020 - 16:03

score 45 · Answer 8 · 2020-04-26 17:52:20

45

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Maximum number of disjoint intervals in the interval $(0,1)$

Published on 26 Apr 2020 - 17:52

score 53 · Answer 9 · 2020-04-26 18:36:08

53

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Arrange according to cardinality.

Published on 26 Apr 2020 - 18:36

score 34 · Answer 10 · 2020-04-26 19:22:30

34

Views

Is there an example for two subsets A and B of the Reals such that cardinality A = card B and card (R-A) does not equal card( R-B )

Published on 26 Apr 2020 - 19:22

score 88 · Answer 11 · 2020-04-27 04:22:03

88

Views

The definition of cardinal exponentiation

Published on 27 Apr 2020 - 4:22

score 84 · Answer 12 · 2020-04-27 04:54:00

84

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Number of random variables in a stochastic process taking a value

Published on 27 Apr 2020 - 4:54

score 200 · Answer 13 · 2020-04-27 07:45:38

200

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The meaning of GCH in ZF

Published on 27 Apr 2020 - 7:45

score 42 · Answer 14 · 2020-04-27 13:21:58

42

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equivalence of two definitions of cardinality

Published on 27 Apr 2020 - 13:21

score 126 · Answer 15 · 2020-04-27 16:19:41

126

Views

What is the cardinality of this infinite group?

Published on 27 Apr 2020 - 16:19

List Question

About Cardinal Exponentiation

If $x$ is a set of cardinality $\kappa$ and $\lambda<\kappa$, do we need the axiom of choice to prove that there is a subset of $x$ of size $\lambda$?

Let $A\subseteq\mathbb{R}$ with $|A|=\omega_1$. Prove $A$ does not embed into $\mathbb{Q}\times\omega_1$.

Let $X\subseteq\mathbb{R}$, and $\forall x\in X, \{y\in X:y>x\}$ is countable. Prove $X$ is countable.

Cardinalities of $\mathbb{R}[X]$ and $\mathbb{R}$

Countable Subset of rational numbers

Continuity of cardinal power function

Maximum number of disjoint intervals in the interval $(0,1)$

Arrange according to cardinality.

Is there an example for two subsets A and B of the Reals such that cardinality A = card B and card (R-A) does not equal card( R-B )

The definition of cardinal exponentiation

Number of random variables in a stochastic process taking a value

The meaning of GCH in ZF

equivalence of two definitions of cardinality

What is the cardinality of this infinite group?

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