inhabited set

A set A is called inhabited, if there exists an element aA. Note that in classical mathematics this is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to A (i.e. A being nonempty), yet in intuitionistic mathematics we actually have to find an element aA. 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.

Title inhabited set
Canonical name InhabitedSet
Date of creation 2013-03-22 14:25:24
Last modified on 2013-03-22 14:25:24
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 6
Author mathwizard (128)
Entry type Definition
Classification msc 03F55