Definition:Initial Segment/Class Theory

Definition
Let $A$ be a class.

Let $\preceq$ be a well-ordering on $A$.

Let $a \in A$.

The initial segment (of $A$) determined by $a$ is defined as:


 * $A_a := \set {b \in S: b \preceq a \land b \ne a}$

which can also be rendered as:


 * $A_a := \set {b \in S: b \prec a}$