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.

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.

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

Distinct means the same thing as different.

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

a distinction can be made between $x$ and $y$

Hence:

$x$ is distinct from $y$

$y$ is distinct from $x$

$x$ and $y$ are distinct from each other.