Definition:Limit Element under Well-Ordering

This page is about Limit Element under Well-Ordering. For other uses, see Limit.

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.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering: Definition $1.5$