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Let $S$ be a set.
The successor (set) of $S$ is defined and denoted:
- $S^+ := S \cup \set S$
Also known as
Some sources use $S'$ rather than $S^+$.
- 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 $1.1$