# Definition:Characteristic Property of Set

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## Definition

Let $S$ be a set which is specified by means of such a propositional function:

- $S = \set {a: \map P a}$

The open statement $\map P x$ is known as a **characteristic property** of $S$.

## Sources

- 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems