Definition
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[1Z0] Let \(X\) be a well-ordered non-empty set. Suppose \(xβ X\) is not the maximum, then the set of majorants \(\{ yβ X:y{\gt}x\} \) is not empty, so we define the successor element \(S(x)\) of \(x\) as
\[ S(x) = \min \{ yβ X:y{\gt}x\} \quad . \]