 (ii) It could provide us with a useful new domain that can be substituted for the integers in any application depending only on equational properties of the integers, but which differs from the integers in other (necessarily nonequational) useful respects. For example the rationals, which satisfy the same laws as we just noted, differ in having the density property, that between any two rationals there lies another rational. Another difference is that it supports division: whereas the ratio of two integers is usually not an integer, the ratio of two rationals is always a rational. The reals also satisfy the same equations, and like the rationals are dense and support division. Unlike the rationals however the reals have the completeness property, that the set of all upper bounds of any nonempty set of reals is either empty or has a least member, needed for convergent sequences to have a limit to converge to.