A sentence is a formula with no free variables.
Simple examples include:
or
However the following formula is not a sentence:
![$\displaystyle \forall x\exists y [x<y]$](http://images.planetmath.org:8080/cache/objects/3387/l2h/img1.png "$\displaystyle \forall x\exists y [x<y]$"){kind=small}
![$\displaystyle \exists z [z+7-43=0]$](http://images.planetmath.org:8080/cache/objects/3387/l2h/img2.png "$\displaystyle \exists z [z+7-43=0]$"){kind=small}
