I am reading Jech's set theory and he defines a cardinal number as an ordinal $\alpha$ (a cardinal) if $|\alpha| \neq |\beta|$ for all $\beta < \alpha$, and he says that all infinite cardinals are limit ordinals. My question is: are there any ordinals that are not cardinals? Although I know that an ordinal describe ordering and a cardinal the size of a set, I am a bit confused here.
Thanks