# 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 $A\neq\emptyset$ (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 InhabitedSet 2013-03-22 14:25:24 2013-03-22 14:25:24 mathwizard (128) mathwizard (128) 6 mathwizard (128) Definition msc 03F55