// note that these definitions illistrate why the iterator template uses three parameters.

    friend class LinkedListIterator<T, T&, T*>;

    friend class LinkedListIterator<T, const T&, const T*>; //Here we want the reference and pointers to be const, but not the data!

    //define some friendly names for veririous versions of the iterator class

    //define some friendly names for various versions of the iterator class

    typedef LinkedListIterator<T, T&, T*> iterator;

    typedef LinkedListIterator<T, const T&, const T*> const_iterator;

    //Allow access to the the template type.. 

    public:

    //Default constructor... set root to null!

    LinkedList() : root(NULL), lastNode(NULL) { }

    //constructor to initilize with a given number of nodes using value_type's default constructor.

    //constructor to initialize with a given number of nodes using value_type's default constructor.

    LinkedList(size_t size) : root(NULL), lastNode(NULL) {

        for(size_t i=0; i < size; ++i) {

            push_top(value_type());

        }

    }

    //constructor to initilize with a given number of nodes with a default value.

    //constructor to initialize with a given number of nodes with a default value.

    //   value_type must have a copy constructor... is this constructor necessary?

    LinkedList(size_t size, value_type defValue) : root(NULL), lastNode(NULL) {

        for(size_t i=0; i < size; ++i) {

            push_top(value_type(defValue));