Set and Maps in STL

Hello,

I'm experiencing a strange problem with STL's set and maps (probably I'm
misusing the container).

When I instantiate a type like this:

std::set<CMyclass> myset;

I'm required to define an operator < for CMyclass in order for the set
(and map) to work.

However I'm wondering why I am not forced to define also an operator ==
(if I do, it is ignored) since to check whether a certain object is in
the set I need to test for exact match and not only for a greater/lesser
relation.

For example:

CMyclass A;

// fill A with proper data
// ...

// check whether the same object is already in myset
if(myset.find( A ) == myset.end()) {
    // object not present, insert it
    myset.insert( A )
    // process object since it's the first time I see it
    // ...
} else {
    // object has already been seen, just ignore it!
    // ...
}

My class for example can hold the coordinates of a pixel

class CMyclass {
public:
    double x,y;

    bool operator<(const CMyclass &P) const
    {
        if(x != P.x) return x < P.x;
        return y < P.y;
    }
};

Regards,
Giuliano Bertoletti