Question

$\alpha + \beta=\beta \iff \alpha\omega\le\beta$: is my proof correct?

score 83 · Answer 1 · 2026-04-16 21:48:50

83

Views

$\alpha + \beta=\beta \iff \alpha\omega\le\beta$: is my proof correct?

Published on 16 Apr 2026 - 21:48

score 115 · Answer 2 · 2026-04-16 19:57:51

115

Views

Does Wolfram's MathWorld describe a different kind of ordinal multiplication?

Published on 16 Apr 2026 - 19:57

score 287 · Answer 3 · 2026-04-15 10:18:31

287

Views

For what ordinals does $1+\alpha=\alpha$ hold? For what ordinals does $2\alpha=\alpha$ hold?

Published on 15 Apr 2026 - 10:18

score 99 · Answer 4 · 2026-04-09 16:17:49

99

Views

Ordinal with cofinality $\Omega_\omega$?

Published on 09 Apr 2026 - 16:17

score 95 · Answer 5 · 2026-04-16 01:14:05

95

Views

$\alpha\ge 2\Rightarrow \alpha^{\beta}\ge\alpha\beta$: is my proof correct?

Published on 16 Apr 2026 - 1:14

score 693 · Answer 6 · 2026-04-13 12:12:06

693

Views

Is the cardinality of two countably infinite, order-isomorphic sets equal?

Published on 13 Apr 2026 - 12:12

score 77 · Answer 7 · 2026-04-09 09:30:47

77

Views

Given ordinal $\alpha \geq \omega_1$ does $\alpha \omega_1 = \omega_1 \alpha$

Published on 09 Apr 2026 - 9:30

score 100 · Answer 8 · 2026-04-14 13:39:21

100

Views

prove that for an ordinal $\alpha \notin \alpha$

Published on 14 Apr 2026 - 13:39

score 400 · Answer 9 · 2026-05-02 20:17:32

400

Views

Where does this array-based fast-growing function fall in the fast-growing hierarchy, and how does it compare to TREE(n)?

Published on 02 May 2026 - 20:17

score 73 · Answer 10 · 2026-04-11 20:22:02

73

Views

In Set Theory what's $0^0$ in terms of ordinals?

Published on 11 Apr 2026 - 20:22

score 65 · Answer 11 · 2026-04-15 22:02:17

65

Views

If $x$ is a set of ordinals, then $\bigcup x=\alpha$. Why is $x\subseteq \alpha+1$ rather than $\alpha$

Published on 15 Apr 2026 - 22:02

score 1000 · Answer 12 · 2026-04-15 06:32:12

1000

Views

Commutativity of Ordinal Multiplication

Published on 15 Apr 2026 - 6:32

score 353 · Answer 13 · 2026-04-11 19:13:40

353

Views

Prove that $\omega$ is not successor ordinal

Published on 11 Apr 2026 - 19:13

score 981 · Answer 14 · 2026-04-15 11:52:24

981

Views

Proving that the class of all ordinals is well ordered under $\in$

Published on 15 Apr 2026 - 11:52

score 85 · Answer 15 · 2026-04-14 13:04:36

85

Views

Exponentially-closed ordinals

Published on 14 Apr 2026 - 13:04

List Question

$\alpha + \beta=\beta \iff \alpha\omega\le\beta$: is my proof correct?

Does Wolfram's MathWorld describe a different kind of ordinal multiplication?

For what ordinals does $1+\alpha=\alpha$ hold? For what ordinals does $2\alpha=\alpha$ hold?

Ordinal with cofinality $\Omega_\omega$?

$\alpha\ge 2\Rightarrow \alpha^{\beta}\ge\alpha\beta$: is my proof correct?

Is the cardinality of two countably infinite, order-isomorphic sets equal?

Given ordinal $\alpha \geq \omega_1$ does $\alpha \omega_1 = \omega_1 \alpha$

prove that for an ordinal $\alpha \notin \alpha$

Where does this array-based fast-growing function fall in the fast-growing hierarchy, and how does it compare to TREE(n)?

In Set Theory what's $0^0$ in terms of ordinals?

If $x$ is a set of ordinals, then $\bigcup x=\alpha$. Why is $x\subseteq \alpha+1$ rather than $\alpha$

Commutativity of Ordinal Multiplication

Prove that $\omega$ is not successor ordinal

Proving that the class of all ordinals is well ordered under $\in$

Exponentially-closed ordinals

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