Revision as of 02:01, 6 September 2022 (edit) OfficialURL (talk \| contribs) No edit summary ← Older edit		Revision as of 02:09, 6 September 2022 (edit) (undo) OfficialURL (talk \| contribs) (Added properties) Newer edit →
Line 1: {{DISPLAYTITLE:\(\omega\)}} The [[ordinal]] '''~~\(\~~omega\)''', ~~(also~~written "\(\omega"\), is ~~the~~defined ~~first [[infinite ordinal]], first [[limit ordinal]], and first [[admissible ordinal]]. It is~~as the [[order type]] of the natural numbers ~~<math>~~\(\mathbb N~~</math>~~\). As a [[von Neumann ordinal]], it corresponds to the naturals themselves. ==Properties== * It is the first [[infinite]] ordinal. * It is the first [[limit ordinal]]. * It is the first [[admissible ordinal]]. * Using the [[von Neumann cardinal assignment]], it is equal to [[aleph 0\|\(\aleph_0\)]]. * It is the smallest ordinal \(\alpha\) such that \(1+\alpha=\alpha\). Every ordinal larger than it has this same property. * It is the next ordinal after [[0]] that isn't a [[successor ordinal]].

Omega: Difference between revisions

Omega (edit)