ABSTRACT
In mathematics, a two-place relation is simply a set of ordered pairs. Since "ordered pair" has just been defined in terms of "unordered pair", and "unordered pairs" are simply sets, it follows that "relation" can be defined in terms of the one primitive notion set. Rational numbers are naturally identified with ordered pairs of natural numbers with no common divisor; and real numbers may be identified with series of rational numbers where a "series" is just a function whose domain is the natural numbers. Thus all of the "objects" of pure mathematics may be built up starting with the one notion set; indeed, this is the preferred style in contemporary mathematics. In general, the mathematicians and philosophers say that a set should never be defined in terms of a "totality" unless that totality is incapable of containing that set, or any set defined in terms of that set.
