- A set $A=\{a\}$ with just one element is obviously well-ordered with respect to $\in$, but in general is not transitive, because $A$ should include the elements of $a$. In fact, the only ordinal with just one element is $1=\{\varnothing\}$
- Each natural number is an ordinal
- The set $\mathbb{N}$ of natural numbers is an ordinal