const problem

MS Developer Studio 7.

I ran in to this experimenting with STL sets the first time. Had it not
been for sample code on page 295 of The C++ Standard Library by Nicolai
Josuttis, I nver would have solved it. The compiler error just didn't give
me the help I needed to figure out what was wrong. Here is the smallest
code snippet I can craft that produces the error:

#include <set>
using namespace std;

struct MyElem {
     int value;
};

struct MyCompare
{
     bool operator() ( const MyElem& elem1, const MyElem& elem2 )
     {
          return( elem1.value < elem2.value );
     }
};

void main()
{
     MyElem myElem;
     int count;

     set<MyElem, MyCompare> MySet;
     count = MySet.erase( myElem );
}

That code produces this cryptic compile time error message

c:\Program Files\Microsoft Visual Studio .NET 2003\Vc7\include\xtree(992) :
error C3848: expression having type 'const MyCompare' would lose some
const-volatile qualifiers in order to call 'bool MyCompare::operator
()(const MyElem &,const MyElem &)'
        c:\Program Files\Microsoft Visual Studio .NET
2003\Vc7\include\xtree(987) : while compiling class-template member function
'std::_Tree<_Traits>::_Nodeptr std::_Tree<_Traits>::_Lbound(const
std::_Tree<_Traits>::key_type &) const'
        with
        [
            _Traits=std::_Tset_traits<MyElem,MyCompare,std::allocator<MyElem>,false>
        ]
        c:\Program Files\Microsoft Visual Studio .NET
2003\Vc7\include\set(57) : see reference to class template instantiation
'std::_Tree<_Traits>' being compiled
        with
        [
            _Traits=std::_Tset_traits<MyElem,MyCompare,std::allocator<MyElem>,false>
        ]
        h:\BAC\win32\misc2\misc2.cpp(120) : see reference to class template
instantiation 'std::set<_Kty,_Pr>' being compiled
        with
        [
            _Kty=MyElem,
            _Pr=MyCompare
        ]

The error doesn't point to my code, but rather to STL code. I finally
figured out what the problem was by trial and error and comparing to that
book example I mentioned. It turned out that this line:

     bool operator() ( const MyElem& elem1, const MyElem& elem2 )

should have a 3rd "const" on it at the end as in:

     bool operator() ( const MyElem& elem1, const MyElem& elem2 ) const

Adding that last const completely eliminated the compiler errors.

I know what the first 2 const's do. My question is what does the 3rd const
mean and why is it required in this case?

Thanks,
Bruce.