# Definition:Limit Element under Well-Ordering

## Definition

Let $A$ be a class.

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

Let $x$ be neither the smallest element of $A$ nor an immediate successor of any element of $A$.

Then $x$ is a limit element of $A$ (under $\preccurlyeq$).

## Also see

• Results about limit elements can be found here.