The original text is meant to mean a triple of statements: x < y if and only if w < z x = y if and only if w = z x > y if and only if w > z This can be tire

The original text is meant to mean a triple of statements: x < y if and only if w < z x = y if and only if w = z x > y if and only if w > z This can be tiresome (and obviously confusing) if you need to keep using it in many places, hence some authors define the odd symbol to start with, and then use that in many places.