Mathematically a class is densely or compactly ordered if between any two distinct members there is always another not identical with either of them. A class is continuously ordered if every non-empty subset that has an upper bound has a least upper bound; intuitively, there are no leaps. (One might say that some philosophical writing appears to confuse density with continuity.) A function f is continuous at a point c if f(x) → f(c) as x → c.