Equivalence Class/Examples/People of Same Age

Example of Equivalence Relation

Let $P$ be the set of people.

Let $\sim$ be the relation on $P$ defined as:

$\forall \tuple {x, y} \in P \times P: x \sim y \iff \text { the age of $x$ and $y$ on their last birthdays was the same}$

Then the equivalence class of $x \in P$ is:

$\eqclass x \sim = \set {\text {All people the same age as $x$ on their last birthday} }$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.4$. Equivalence classes