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Of Two or More Objects

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.

Of a Single Object

Let $x \in S$ be an element of a set of objects $S$.


$x$ is distinguished from the other elements of $S$

if and only if

$x$ is endowed with a property that the other elements of $S$ are specifically deemed not to possess.

Such an element is identified as being distinct from the others.


Two objects are indistinguishable if they can not (in a particular context) be told apart from each other.

So, two objects may be distinct but (at a given level) indistinguishable, like identical twins.

Also see