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I am trying to define a uniqueness of a member of a set, please bear with me as my notation is not as refined as it ought to be:

For a set X:

{ x(i) } union { f(x(j)) = true, where j is not equal to i } = { x(i) }

what I am trying to say is, for this set X there exists only one member whose evaluation with f() results in true.

I am defining this by saying that the union of any element with any other element other than itself in the set who's value is true is equal to the first element, however this doesn't quite work - I almost need a count() function on the right side and say that the count() is always = 1.

Is there a more correct elegant way to say this?

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# Membership Uniqueness?

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