Inhabited set
Encyclopedia : I : IN : INH : Inhabited set
A set A is called inhabited if there exists an element [a\in A.] Note that in classical mathematics this is equivalent to [A\neq\emptyset] (A being nonempty), yet in intuitionistic mathematics we actually have to find an element [a\in A.]. For example the set, which contains 1 if Goldbach's conjecture is true and 0 if it is false is certainly nonempty, yet by today's state of knowledge we cannot say if A is inhabited, since we do not know an element of [A.]
See also
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