Linear continuum

In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line.

Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered, i.e., between any two distinct elements there is another (and hence infinitely many others), and which "lacks gaps" in the sense that every non-empty subset with an upper bound has a least upper bound. More symbolically: