Definition:Immediate Successor Element/Class Theory

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

Let $a, b \in A$.

Then $a$ is an immediate successor (element) to $b$ $b$ is an immediate predecessor (element) to $a$.

That is, :
 * $(1): \quad b \prec a$
 * $(2): \quad \nexists c \in S: b \prec c \prec a$

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

Also see

 * Definition:Immediate Predecessor Element (Class Theory)


 * Immediate Successor under Total Ordering is Unique
 * Non-Maximal Element of Well-Ordered Class has Immediate Successor