Variation with repetitions into null set.

Variation with repetitions into null set.

Let's consider a set with the following elements:
S = {a, b, c}
If we have D = 2 place holders for each element of set S and there maight
be repetitions and the order is relevant, then we have the following set
of results:
{a, a}
{a, b}
{a, c}
{b, a}
{b, b}
{b, c}
{c, a}
{c, b}
{c, c}
The general pattern is |R| = |S|^|D|.
Now, let us consider two extremes.
S = {}, |S| = 0, |D| > 0. What is the result? R = {}, |R| = 0^|D| = 0.
That I understand. There is no elements in the source S, so the result set
R exists and is empty.
S = {a, b, c}, |S| = 3, |D| = 0. What is the result? |R| = 3^0 = 1. Hm,
What? R is not empty? What element should be in R?