Inhabited set
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A set A is called inhabited if there exists an element 
Note that in classical mathematics this is equivalent to 
(A being nonempty), yet in intuitionistic mathematics we actually have to find an element . 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.
[edit] See also
This article incorporates material from Inhabited set on PlanetMath, which is licensed under the GFDL.
