Definition:Successor Mapping/Successor Set
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Let $V$ be a basic universe.
Let $s: V \to V$ denote the successor mapping on $V$.
For $x \in V$, the result of applying the successor mapping on $x$ is denoted $x^+$:
- $x^+ := \map s x = x \cup \set x$
$x^+$ is referred to as the successor (set) of $x$.
- Results about the successor mapping can be found here.
- 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 11$: Numbers
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 7.22$
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 1$ Preliminaries: Definition $1.1$