Successor ordinal: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "An ordinal is called a successor if it is equal to \(\alpha + 1\) for some other \(\alpha\). An ordinal \(\alpha\) is a successor if and only if \(\max \alpha\) exists. The smallest successor ordinal is 1, which is also the only successor ordinal to also be additively principal. The least ordinal that is not a successor, other than 0, is \(\omega\). If \(\beta\) is successor, then \(\alpha+\beta\) is also successor f...") |
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An [[ordinal]] is called a successor if it is equal to \(\alpha + 1\) for some other \(\alpha\). An ordinal \(\alpha\) is a successor if and only if \(\max \alpha\) exists. The smallest successor ordinal is [[1]], which is also the only successor ordinal to also be [[Additive principal ordinals|additively principal]]. The least ordinal that is not a successor, other than [[0]], is [[Omega|\(\omega\)]].
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