Recall that an infinite set is countable if it is bijectable, i.e., it can be put into a one-to-one correspondence, with \(\omega\). All the ordinals displayed above are either finite or countable. But the set of all finite and countable ordinals is also an ordinal, called \(\omega_1\), and is not countable. Similarly, the set of all ordinals that are bijectable with some ordinal less than or equal to \(\omega_1\) is also an ordinal, called \(\omega_2\), and is not bijectable with \(\omega_1\), and so on.