: The first sentence is a description of a Cartesian geometry, not of an ordered pair.  An ordered pair of coordinates is an attribute of an object in Cartesian geometry, not the object itself, and certainly not a "collection" of such objects.
 An attempt to improve this muddle was recently 'corrected' with this note: "distinguished" was incorrect, both objects can be the same, i.e. indistinguishable.  So what?  If two coordinates happen to have equal values, they are still distinguished by their function. —