C++: Little teaser about std::set

This does not build. Can you guess why? Without testing it?

std::set< int > numbers;

for (int i = 0; i < 10; i++)
   numbers.insert(i);

for (std::set< int >::iterator iter = numbers.begin();
    iter != numbers.end(); iter++) {
   int& i = *iter;
   i++;
}

Update (23:40): John gave a correct answer in the comments.