# Definition:Distinct/Plural

## Definition

Two objects $x$ and $y$ are distinct if and only if $x \ne y$.

If $x$ and $y$ are distinct, then that means they can be distinguished, or identified as being different from each other.

## Pairwise Distinct

A set $S$ of objects is pairwise distinct if and only if:

for each pair $\set {x, y} \subseteq S$ of elements of $S$, $x$ and $y$ are distinct.

## Also defined as

Some sources restrict the scope of this definition to mean not numerically equal.

## Also known as

Distinct means the same thing as different.

If $x$ and $y$ are distinct then:

a distinction can be made between $x$ and $y$
$x$ is distinct from $y$; $y$ is distinct from $x$; $x$ and $y$ are distinct from each other.