Definition:Limit Element under Well-Ordering
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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 $1.5$