First uncountable ordinal

Summary

In mathematics, the first uncountable ordinal, traditionally denoted by $\omega_1$ or sometimes by $\Omega$, is the smallest ordinal number that is the order type of an uncountable well-ordered set. It is the supremum (least upper bound) of all countable ordinals. In the von Neumann representation, the elements of $\omega_1$ are the countable ordinals (including finite ordinals), of which there are uncountably many.