A limit cardinal is a cardinal $\kappa$ such that $\lambda^+<\kappa$ for every cardinal $\lambda<\kappa$ Here $\lambda^+$ denotes the cardinal successor of $\lambda$ If $2^\lambda<\kappa$ for every cardinal $\lambda<\kappa$ then $\kappa$ is called a strong limit cardinal.

Every strong limit cardinal is a limit cardinal, because $\lambda^+\leq2^\lambda$ holds for every cardinal $\lambda$ Under GCH, every limit cardinal is a strong limit cardinal because in this case $\lambda^+=2^\lambda$ for every infinite cardinal $\lambda$

The three smallest limit cardinals are $0$ $\aleph_0$ and $\aleph_\omega$ Note that some authors do not count $0$ or sometimes even $\aleph_0$ as a limit cardinal. An infinite cardinal $\aleph_\alpha$ is a limit cardinal if and only if $\alpha$ is a limit ordinal (counting $0$ as a limit ordinal).