adj. 1. (of a set in an ordered space) having the property that between any two comparable elements a third can be interposed. Thus the rational numbers are dense, since for any rationals a and b, 1/2(a + b) lies between them and is also a rational. 2. (of a set in a topology) having a closure that contains a given set. More simply, one set is dense in another if the second is contained in the closure of the first. For example, the rationals are dense in the reals, since the latter are contained in the closure of the former. 3. (of a matrix) see sparse.