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 $A\ne \mathrm{\varnothing }$ (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 $A$.

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