...
- For all
x
:x < x == false
(irreflexivity) - For all
x
,y
: ifx < y
then!(y < x)
(asymmetry) - For all
x
,y
,z
: ifx < y && y < z ==
thenx < z
(transitivity)
Providing an invalid ordering predicate for an associative container, or as a comparison criterion with the sorting algorithms, can result in erratic behavior or infinite loops [Meyers 01]. When an ordering predicate is required for an associative container or a generic standard template library algorithm, the predicate must meet the requirements for inducing a strict weak ordering.
...