Example 4.7.1.9 (Finite Ordinals). Let $n$ be a nonnegative integer. Up to isomorphism, there is a unique linearly ordered set $S$ having exactly $n$ elements, which we can identify with the set $\{ 0 < 1 < \cdots < n-1 \} $. We will abuse notation by identifying $n$ with the order type of the linearly ordered set $S$. By means of this convention, we can view every nonnegative integer as an ordinal. We say that an ordinal $\alpha $ is finite it arises in this way (that is, if it is the order type of a finite linearly ordered set), and infinite if it does not.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$