Question

Is there a reasonable way of defining the surreal number $\aleph_{-1}$ or $\omega_{-1}$?

score 798 · Answer 1 · 2026-03-25 07:44:46

798

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Is there a reasonable way of defining the surreal number $\aleph_{-1}$ or $\omega_{-1}$?

Published on 25 Mar 2026 - 7:44

score 43 · Answer 2 · 2020-05-30 16:37:21

43

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Prove that $\alpha \cup \{\alpha \} = \text {inf}\ \{\beta\ \mid\ \beta \gt \alpha \}.$

Published on 30 May 2020 - 16:37

score 57 · Answer 3 · 2020-05-30 18:25:12

57

Views

Is this fact about ordinals true?

Published on 30 May 2020 - 18:25

score 103 · Answer 4 · 2020-06-02 14:56:01

103

Views

Find the smallest ordinal $ \gamma $ that satisfies $ \omega+\gamma=\gamma $

Published on 02 Jun 2020 - 14:56

score 146 · Answer 5 · 2026-03-28 01:35:20

146

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Theory of the von Neumann hierarchy

Published on 28 Mar 2026 - 1:35

score 105 · Answer 6 · 2026-03-25 07:49:09

105

Views

Cauchy completion of transfinite "rationals"

Published on 25 Mar 2026 - 7:49

score 73 · Answer 7 · 2020-06-06 12:56:37

73

Views

For which function are the fixed-points enumerated by $\phi_0(\alpha)$?

Published on 06 Jun 2020 - 12:56

score 238 · Answer 8 · 2020-06-08 03:28:23

238

Views

For ordinals $\delta$ and $\beta$, if $\delta\in$ or $=\beta$, then there exists $\gamma\in$ or $=\beta$ such that $\beta=\delta+\gamma$

Published on 08 Jun 2020 - 3:28

score 142 · Answer 9 · 2026-03-26 12:48:22

142

Views

Hessenberg power of ordinals (redux)

Published on 26 Mar 2026 - 12:48

score 124 · Answer 10 · 2020-06-09 18:38:13

124

Views

Let $\alpha$ be a limit ordinal. $f: \alpha \to \beta $ be strictly increase cofinal map. then $cf(\alpha) = cf(\beta)$.

Published on 09 Jun 2020 - 18:38

score 113 · Answer 11 · 2020-06-11 12:47:28

113

Views

Explicit formulas for natural (Hessenberg) and ordinal sum: Do those work?

Published on 11 Jun 2020 - 12:47

score 80 · Answer 12 · 2020-06-12 09:18:59

80

Views

Given $\kappa = \sup_{\alpha< \lambda} \kappa_{\alpha}$n can we assume the $\{\kappa_\alpha: \alpha < \lambda\}$ is strictly increasing?

Published on 12 Jun 2020 - 9:18

score 73 · Answer 13 · 2020-06-12 13:01:29

73

Views

For $\alpha + \beta \;$ limit ordinal, $\alpha, \beta > 0\;$ are ordinals, show that $\beta$ is a limit ordinal

Published on 12 Jun 2020 - 13:01

score 122 · Answer 14 · 2020-06-12 18:55:10

122

Views

Finding real-numbers subsets which are isomorphic to some ordinals.

Published on 12 Jun 2020 - 18:55

score 195 · Answer 15 · 2020-06-12 20:40:26

195

Views

Class of Successor ordinals.

Published on 12 Jun 2020 - 20:40

List Question

Is there a reasonable way of defining the surreal number $\aleph_{-1}$ or $\omega_{-1}$?

Prove that $\alpha \cup \{\alpha \} = \text {inf}\ \{\beta\ \mid\ \beta \gt \alpha \}.$

Is this fact about ordinals true?

Find the smallest ordinal $ \gamma $ that satisfies $ \omega+\gamma=\gamma $

Theory of the von Neumann hierarchy

Cauchy completion of transfinite "rationals"

For which function are the fixed-points enumerated by $\phi_0(\alpha)$?

For ordinals $\delta$ and $\beta$, if $\delta\in$ or $=\beta$, then there exists $\gamma\in$ or $=\beta$ such that $\beta=\delta+\gamma$

Hessenberg power of ordinals (redux)

Let $\alpha$ be a limit ordinal. $f: \alpha \to \beta $ be strictly increase cofinal map. then $cf(\alpha) = cf(\beta)$.

Explicit formulas for natural (Hessenberg) and ordinal sum: Do those work?

Given $\kappa = \sup_{\alpha< \lambda} \kappa_{\alpha}$n can we assume the $\{\kappa_\alpha: \alpha < \lambda\}$ is strictly increasing?

For $\alpha + \beta \;$ limit ordinal, $\alpha, \beta > 0\;$ are ordinals, show that $\beta$ is a limit ordinal

Finding real-numbers subsets which are isomorphic to some ordinals.

Class of Successor ordinals.

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