I am working in Keith Devlin's Second Edition: Joy of Sets. Page. 18, after Theorem 1.7.3. He writes as follows: " Let $(X,\leq)$ be a woset (i.e. well-ordered set), $a \in X$. By segment $X_a$ of $X$ determined by $a$ we mean the set:
$X_a = \{ x \in X \mid x < a \}$
Very unclear as to what this means exactly. It is not the same thing as taking a segment of a line? The idea becomes important very quickly with Ordinality.
Devlin writes: "An ordinal is defined to be a woset $(X,\leq)$ such that $X_a = a$ for all $a$ in $X$." Again: the meaning is not clear to me.
Thank you for the help!