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The cofinality of an ordinal is the length of the shortest possible sequence leading up to it from below[citation needed]. For example, the cofinality of $$\omega2$$ is $$\omega$$ because of the sequence $$\omega,\omega+1,\omega+2,\omega+3,\cdots$$.

The cofinality of any countable limit ordinal is ω[1]. The cofinality of any successor ordinal is 1[2]. The cofinality of 0 is 0.

## Regular

An ordinal is called regular if its cofinality equals itself.

1. P. Nadathur, To Infinity And Beyond (p.27) (accessed 2021-03-15)
2. P. Nadathur, To Infinity And Beyond (p.27) (accessed 2021-03-15)