Question

Showing that $\aleph_0^{|2^\mathbb{N}|} > |2^\mathbb{N}|$

score 45 · Answer 1 · 2026-04-15 09:12:01

45

Views

Showing that $\aleph_0^{|2^\mathbb{N}|} > |2^\mathbb{N}|$

Published on 15 Apr 2026 - 9:12

score 243 · Answer 2 · 2026-04-14 05:32:18

243

Views

Cantor’s Diagonalization For Other Lists

Published on 14 Apr 2026 - 5:32

score 98 · Answer 3 · 2026-04-12 19:00:00

98

Views

Cardinality and Countably Infinite

Published on 12 Apr 2026 - 19:00

score 133 · Answer 4 · 2026-04-12 19:18:28

133

Views

Axiom of Choice: General associative and commutative law for infinite sum/product of cardinals

Published on 12 Apr 2026 - 19:18

score 58 · Answer 5 · 2026-04-17 01:53:25

58

Views

If $|A|>|B|$, then there exists a $C\subseteq A$ such that $|C|=|B|$.

Published on 17 Apr 2026 - 1:53

score 105 · Answer 6 · 2026-04-16 15:46:57

105

Views

Partitioning Infinite Set $M$ to Countable Sets Each with the Same Cardinality as $M$

Published on 16 Apr 2026 - 15:46

score 65 · Answer 7 · 2026-04-17 08:49:06

65

Views

$\alpha ,\beta $ cardinals such that $2\leq \alpha \leq \beta $. Prove : $ \beta^{\beta^\alpha} \leq \alpha^{\alpha^\beta}$

Published on 17 Apr 2026 - 8:49

score 91 · Answer 8 · 2026-04-14 01:32:51

91

Views

Cardinality of set of Baire functions

Published on 14 Apr 2026 - 1:32

score 166 · Answer 9 · 2026-04-17 15:33:46

166

Views

$|X| \le |Y|$ iff there is a injection from $X$ to $Y$

Published on 17 Apr 2026 - 15:33

score 133 · Answer 10 · 2026-04-11 19:02:27

133

Views

Is it sufficient to find an injective function and a surjective function to show cardinality of two sets is equal?

Published on 11 Apr 2026 - 19:02

score 59 · Answer 11 · 2026-04-15 06:39:40

59

Views

The set of countable subsets is countable

Published on 15 Apr 2026 - 6:39

score 439 · Answer 12 · 2026-04-16 01:18:03

439

Views

Prove $\text{cf}(\aleph_{\omega}) = \text{cf}(\aleph_{\omega + \omega}) = \omega$ and $\text{cf}(\aleph_{\omega_{1}}) = \omega_{1}$.

Published on 16 Apr 2026 - 1:18

score 41 · Answer 13 · 2026-04-12 00:41:50

41

Views

About $\kappa^\mu = \kappa$, where $\kappa,\mu$ are cardinals.

Published on 12 Apr 2026 - 0:41

score 119 · Answer 14 · 2026-04-14 09:37:31

119

Views

Cardinality of set of well-ordered sequences

Published on 14 Apr 2026 - 9:37

score 63 · Answer 15 · 2026-04-13 01:05:11

63

Views

Induction over other sets

Published on 13 Apr 2026 - 1:05

List Question

Showing that $\aleph_0^{|2^\mathbb{N}|} > |2^\mathbb{N}|$

Cantor’s Diagonalization For Other Lists

Cardinality and Countably Infinite

Axiom of Choice: General associative and commutative law for infinite sum/product of cardinals

If $|A|>|B|$, then there exists a $C\subseteq A$ such that $|C|=|B|$.

Partitioning Infinite Set $M$ to Countable Sets Each with the Same Cardinality as $M$

$\alpha ,\beta $ cardinals such that $2\leq \alpha \leq \beta $. Prove : $ \beta^{\beta^\alpha} \leq \alpha^{\alpha^\beta}$

Cardinality of set of Baire functions

$|X| \le |Y|$ iff there is a injection from $X$ to $Y$

Is it sufficient to find an injective function and a surjective function to show cardinality of two sets is equal?

The set of countable subsets is countable

Prove $\text{cf}(\aleph_{\omega}) = \text{cf}(\aleph_{\omega + \omega}) = \omega$ and $\text{cf}(\aleph_{\omega_{1}}) = \omega_{1}$.

About $\kappa^\mu = \kappa$, where $\kappa,\mu$ are cardinals.

Cardinality of set of well-ordered sequences

Induction over other sets

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