"undefined reference to" with a fully static class

Question

The following code

#include <iostream>

class X          // fully static class
{
  private:
     static int x;
  public:
     static int get()
     {
         return x;
     }
     static void set(int i)
     {
         x = i;
     }
};


int main()
{
    X::set(3);
    std::cout << X::get() << std::endl;

    return 0;
}

leads to what looks like a linking problem while compiling

undefined reference to `X::x'

What is causing this problem?