HashSet with Index Access

Question

I would need a data structure that

1. Allows me to add/item to it
2. Do not allow duplication
3. access the collection via index

I am t

Answer 1

does it work?

class MyHashSet : HashSet
{
    public T this[int index]
    {
        get
        {
            int i = 0;
            foreach (T t in this)
            {
                if (i == index)
                    return t;
                i++;
            }
            throw new IndexOutOfRangeException();
        }
    }
}