Note that every ordinal is the set of its predecessors. However, the class \(ON\) of all ordinals is not a set. Otherwise, \(ON\) would be an ordinal greater than all the ordinals, which is impossible. The first infinite ordinal, which is the set of all finite ordinals, is denoted by the Greek letter omega (\(\omega\)). In ZFC, one identifies the finite ordinals with the natural numbers. Thus, \({\varnothing}=0\), \(\{ {\varnothing}\}=1\), \(\{ {\varnothing}, \{ {\varnothing}\}\}=2\), etc., hence \(\omega\) is just the set \(\mathbb{N}\) of natural numbers.