First uncountable ordinal

Smallest ordinal number that, considered as a set, is uncountable

In mathematics, the first uncountable ordinal, traditionally denoted by ω 1 {\displaystyle \omega _{1}} or sometimes by Ω {\displaystyle \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.