Question

Isomorphism between the first the uncountable ordinal $\omega_{1}$ and real numbers

score 100 · Answer 1 · 2026-04-11 22:41:53

100

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Isomorphism between the first the uncountable ordinal $\omega_{1}$ and real numbers

Published on 11 Apr 2026 - 22:41

score 93 · Answer 2 · 2026-04-14 16:59:28

93

Views

$\operatorname{cf}(\sup(B \cap \omega_m))$ is the natural numbers

Published on 14 Apr 2026 - 16:59

score 68 · Answer 3 · 2026-04-15 10:20:36

68

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The cardinality of the preimage of an ordinal

Published on 15 Apr 2026 - 10:20

score 382 · Answer 4 · 2026-04-08 16:28:03

382

Views

Questions about $\omega_1$ as a space (The Set of All Countable Ordinals)

Published on 08 Apr 2026 - 16:28

score 70 · Answer 5 · 2026-04-13 10:35:14

70

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Is $\aleph_0 - n$ defined for finite $n$?

Published on 13 Apr 2026 - 10:35

score 168 · Answer 6 · 2026-04-15 02:43:50

168

Views

Correct cardinals vs Stable ordinals

Published on 15 Apr 2026 - 2:43

score 47 · Answer 7 · 2026-04-16 02:43:10

47

Views

Prove that if $X$ is finite then $f[X]$ is finite for any function $f:X\rightarrow Y$ and $|f[X]|\le |X|$.

Published on 16 Apr 2026 - 2:43

score 472 · Answer 8 · 2026-04-13 23:58:55

472

Views

How to write proof for there is no injective function from $[0, 1]$ to $\mathbb{N}$?

Published on 13 Apr 2026 - 23:58

score 133 · Answer 9 · 2026-04-10 07:27:58

133

Views

About the definition of hereditary cardinality

Published on 10 Apr 2026 - 7:27

score 58 · Answer 10 · 2026-04-15 15:00:53

58

Views

Find the smallest cardinal $\kappa$ such that $\omega + \omega$ is the supremum of $\kappa$ smaller ordinals

Published on 15 Apr 2026 - 15:00

score 110 · Answer 11 · 2026-04-15 05:14:43

110

Views

Cardinality of $\mathbb N^{\mathbb N}$ is equal to $\mathbb R$

Published on 15 Apr 2026 - 5:14

score 108 · Answer 12 · 2026-04-15 20:31:24

108

Views

Cofinality of functions $\mathbb N\to\mathbb N$ under eventual domination

Published on 15 Apr 2026 - 20:31

score 147 · Answer 13 · 2026-03-25 20:10:54

147

Views

Questions about the induction on cardinals

Published on 25 Mar 2026 - 20:10

score 175 · Answer 14 · 2026-04-15 09:47:54

175

Views

How many monotonic functions on sets of naturals are there?

Published on 15 Apr 2026 - 9:47

score 77 · Answer 15 · 2026-04-11 23:26:52

77

Views

Cardinality Proving Question

Published on 11 Apr 2026 - 23:26

List Question

Isomorphism between the first the uncountable ordinal $\omega_{1}$ and real numbers

$\operatorname{cf}(\sup(B \cap \omega_m))$ is the natural numbers

The cardinality of the preimage of an ordinal

Questions about $\omega_1$ as a space (The Set of All Countable Ordinals)

Is $\aleph_0 - n$ defined for finite $n$?

Correct cardinals vs Stable ordinals

Prove that if $X$ is finite then $f[X]$ is finite for any function $f:X\rightarrow Y$ and $|f[X]|\le |X|$.

How to write proof for there is no injective function from $[0, 1]$ to $\mathbb{N}$?

About the definition of hereditary cardinality

Find the smallest cardinal $\kappa$ such that $\omega + \omega$ is the supremum of $\kappa$ smaller ordinals

Cardinality of $\mathbb N^{\mathbb N}$ is equal to $\mathbb R$

Cofinality of functions $\mathbb N\to\mathbb N$ under eventual domination

Questions about the induction on cardinals

How many monotonic functions on sets of naturals are there?

Cardinality Proving Question

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