The natural numbers are a basis from which many other number sets may be built by extension: the integers, by including (if not yet in) the neutral element 0 and an additive inverse (−) for each nonzero natural number ; the rational numbers, by including a multiplicative inverse () for each nonzero integer (and also the product of these inverses by integers); the real numbers by including with the rationals the limits of (converging) Cauchy sequences of rationals; the complex numbers, by including with the real numbers the unresolved square root of minus one (and also the sums and products thereof); and so on. These chains of extensions make the natural numbers canonically embedded (identified) in the other number systems.