Under the hyperreal number system, infinitesimal numbers are nonzero, so then how would it be consistent withRbeing complete?

If completeness axiom says that every bounded set has a least upper bound, then I know that the rationals don't have the completeness property since the open interval from 0 to pi doesn't have a least upper bound inQ. But under the hyperreal system, what about analogous interval from 0 to, say, some infinitesimal plus pi?