  We prove that every elementary $(\infty,1)$-topos has a natural number
object. We achieve this by defining the loop space of the circle and showing
that we can construct a natural number object out of it. Part of the proof
involves showing that various definitions of natural number objects (Lawvere,
Freyd and Peano) agree with each other in an elementary $(\infty,1)$-topos. As
part of this effort we also study the internal object of contractibility in
$(\infty,1)$-categories, which is of independent interest. Finally, we discuss
various applications of natural number objects. In particular, we use it to
define internal sequential colimits in an elementary $(\infty,1)$-topos.
