Preorder
Interval

For a ≲ b, {\displaystyle a\lesssim b,} the interval {\displaystyle } is the set of points x satisfying a ≲ x {\displaystyle a\lesssim x} and x ≲ b, {\displaystyle x\lesssim b,} also written a ≲ x ≲ b. {\displaystyle a\lesssim x\lesssim b.} It contains at least the points a and b. One may choose to extend the definition to all pairs (a, b) {\displaystyle (a,b)} The extra intervals are all empty.

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

Also {\displaystyle (a,b]} can be defined similarly.
detectable_format:multiple_sections[4], detectable_content:postscript