Question

Can you ﬁnd a set $A$ which satisﬁes $A = \{2,|A|\}$?

score 309 · Answer 1 · 2020-04-14 14:37:01

309

Views

Can you ﬁnd a set $A$ which satisﬁes $A = \{2,|A|\}$?

Published on 14 Apr 2020 - 14:37

score 43 · Answer 2 · 2020-04-14 22:26:34

43

Views

What is the cardinality of the set of real numbers in union with the set containing the empty set.

Published on 14 Apr 2020 - 22:26

score 65 · Answer 3 · 2020-04-14 22:57:07

65

Views

Show that $\{x\}^A \approx A$

Published on 14 Apr 2020 - 22:57

score 119 · Answer 4 · 2026-03-25 08:09:47

119

Views

What's the dimension of $K^S$ for arbitrary $S$?

Published on 25 Mar 2026 - 8:09

score 563 · Answer 5 · 2026-03-26 12:40:28

563

Views

How is the Continuum Hypothesis equivalent to the existence of a well-ordering on $\Bbb R$ whose bounded initial segments are countable?

Published on 26 Mar 2026 - 12:40

score 153 · Answer 6 · 2020-04-18 16:27:16

153

Views

Cardinality of $\mathcal{P}(\mathbb{N})$ and $\mathbb{R}$

Published on 18 Apr 2020 - 16:27

score 1.3k · Answer 7 · 2026-03-28 03:58:42

1.3k

Views

What are $\aleph_0$, $\omega$ and $\mathbb{N}$ and how are they related to each other?

Published on 28 Mar 2026 - 3:58

score 1.9k · Answer 8 · 2026-03-28 19:39:57

1.9k

Views

What is an weakly compact cardinal?

Published on 28 Mar 2026 - 19:39

score 30 · Answer 9 · 2020-04-19 13:32:18

30

Views

Proving cardinal inequality

Published on 19 Apr 2020 - 13:32

score 57 · Answer 10 · 2020-04-20 12:53:28

57

Views

Left and right index in the exponent

Published on 20 Apr 2020 - 12:53

score 52 · Answer 11 · 2020-04-21 03:53:35

52

Views

Show that on an infinite set $X$,the set of all possible metrics has a cardinality of $2^X$.

Published on 21 Apr 2020 - 3:53

score 826 · Answer 12 · 2020-04-21 16:45:08

826

Views

Countability of set of functions from $\mathbb{Q}$ to $ \left \{0,1 \right \}$ under some conditions

Published on 21 Apr 2020 - 16:45

score 94 · Answer 13 · 2020-04-21 18:16:49

94

Views

Proof without ordinals that $\left|\bigcup_{i\in I}C_i\right|\leqslant |I|$?

Published on 21 Apr 2020 - 18:16

score 107 · Answer 14 · 2020-04-22 05:52:40

107

Views

Do all sets of cardinals have a countable subset with the same supremum?

Published on 22 Apr 2020 - 5:52

score 70 · Answer 15 · 2026-03-28 04:00:28

70

Views

$\alpha \in \mathfrak{a}$ implies $\alpha + \mathfrak{a} =\mathfrak{a}$

Published on 28 Mar 2026 - 4:00

List Question

Can you ﬁnd a set $A$ which satisﬁes $A = \{2,|A|\}$?

What is the cardinality of the set of real numbers in union with the set containing the empty set.

Show that $\{x\}^A \approx A$

What's the dimension of $K^S$ for arbitrary $S$?

How is the Continuum Hypothesis equivalent to the existence of a well-ordering on $\Bbb R$ whose bounded initial segments are countable?

Cardinality of $\mathcal{P}(\mathbb{N})$ and $\mathbb{R}$

What are $\aleph_0$, $\omega$ and $\mathbb{N}$ and how are they related to each other?

What is an weakly compact cardinal?

Proving cardinal inequality

Left and right index in the exponent

Show that on an infinite set $X$,the set of all possible metrics has a cardinality of $2^X$.

Countability of set of functions from $\mathbb{Q}$ to $ \left \{0,1 \right \}$ under some conditions

Proof without ordinals that $\left|\bigcup_{i\in I}C_i\right|\leqslant |I|$?

Do all sets of cardinals have a countable subset with the same supremum?

$\alpha \in \mathfrak{a}$ implies $\alpha + \mathfrak{a} =\mathfrak{a}$

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