Definition:Immediate Predecessor Element/Class Theory

Definition
Let $A$ be an ordered class under an ordering $\preccurlyeq$.

Let $a, b \in A$.

Then $a$ is an immediate predecessor (element) to $b$ :
 * $(1): \quad a \prec b$
 * $(2): \quad \neg \exists c \in S: a \prec c \prec b$

We say that $a$ immediately precedes $b$.

Also see

 * Definition:Immediate Successor Element (Class Theory)


 * Immediate Predecessor under Total Ordering is Unique