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 $A\eq\\emptyset$ (i.e. $A$ 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 $A$ .

单词	InhabitedSet
释义	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 $A\eq\\emptyset$ (i.e. $A$ 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 $A$ .
随便看	TopologyInducedByUniformStructure topology induced by uniform structure TopologyOfLocallyConvexSpacesIsGeneratedBySeminorms topology of locally convex spaces is generated by seminorms TopologyOfTheComplexPlane topology of the complex plane TopologyViaConvergingNets topology via converging nets TopTenCoolestNumbers top ten coolest numbers TorricellisTrumpet Torricelli’s trumpet Torsion torsion TorsionElement torsion element TorsionspaceCurve torsion (space curve) Torus torus TotalDifferential total differential TotalIntegralClosure total integral closure TotallyBounded