Set Definition by Predicate/Examples/Even Integers

Examples of Set Definition by Predicate

Let $S$ be the set defined as:

$S := \set {i: \text {$i$ is an integer and there exists an integer $j$ such that $i = 2 j$} }$

Then $S$ is the set of all even integers.

Sources

• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.4$ Set Notation