Definition:Convex Subset of Natural Numbers

Definition

Let $A \subseteq \N$ be a subset of the set of natural numbers.

$A$ is defined as being convex (in $\N$) if and only if:

$\forall x, y, z \in \N: \paren {x, z \in A \land x \le y \le z} \implies y \in A$

Also see

• Definition:Convex Set (Order Theory)

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 11$: Quotient Structures: Exercise $11.20$