Editing Preorder (section)

==Interval==
For <math>a \lesssim b,</math> the [[Interval (mathematics)|interval]] <math>[a, b]</math> is the set of points ''x'' satisfying <math>a \lesssim x</math> and <math>x \lesssim b,</math> also written <math>a \lesssim x \lesssim b.</math> It contains at least the points ''a'' and ''b''. One may choose to extend the definition to all pairs <math>(a, b)</math> The extra intervals are all empty.

Using the corresponding strict relation "<math><</math>", one can also define the interval <math>(a, b)</math> as the set of points ''x'' satisfying <math>a < x</math> and <math>x < b,</math> also written <math>a < x < b.</math> An open interval may be empty even if <math>a < b.</math>

Also <math>[a, b)</math> and <math>(a, b]</math> can be defined similarly.