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relation on the universe, define <math>[x]_R</math> as the set of all y such that <math>y R x</math>
and the [[rank (set theory)|rank]] of y is less than or equal to the rank of any <math>z R x</math>. This works
because the ranks are sets. Of course, there still may be a proper class of <math>[x]_R</math>'s.
In [[NFU]], the main difficulty is that <math>[x]_R</math> is one type higher than x, so for
example the "map" <math>x \mapsto [x]_R</math> is not a (set) function (though <math>\{x\} \mapsto [x]_R</math> is a set). This can be circumvented by the use of the Axiom of Choice to select
a representative from each equivalence class to replace <math>[x]_R</math>, or by choosing
a canonical representative if there is a way to do this without invoking Choice (the use
of representatives is hardly unknown in [[ZFC]], either. In [[NFU]], the use of equivalence
class constructions to abstract properties of general sets is more common, as for example in
the definitions of cardinal and ordinal number below.
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