less or less_equal using set

Question

We can pass a function as <(less) operator to STL data structures such as set, multiset, map, priority_queue, ...

Is there a problem if our function acts like <=(less_equal)?

Answer 1

Yes, there is a problem.

Formally, the comparison function must define a strict weak ordering, and <= does not do that.

more specifically, the < is also used to determine equivalence (x and y are equivalent iff !(x < y) && !(y < x)). This does not hold true for <= (using that operator would have your set believe that objects are never equivalent)