The total number of items (balls) in an object, no matter the color, is known formally as *cardinality.* Despite its sophisticated sounding title, the formula for calculating *cardinality* of a mist is quite simple and derivable from its definition.

**A ‘mist’ is a two-level hierarchical structure:**

Level 1: **(Entry) _{j} j = 1…N (separated by comma), with each entry containing**

Level 2: **(Items) _{k }k = 1…M **

**drawn from set of balls {white, black}**

**with the added restriction that each item contains the same number of balls – that is:
Cardinality (Item)_{a} = Cardinality (Item)_{b}**

Thus, the total number of items (balls) in a mist is a sum of a sum and this double sum turns out to equal the product of the number of items in each of the individual sums. So we have:

**Total Number of Items (balls) In Mist = N x M **

Which is formally called the *cardinality** *of the mist.

Beyond calculating the outcome of two objects, we also acknowledge the *process* used with a fancy formal name – *Cartesian Product. *

But why stop at two objects such as ‘entries’ and ‘items’? The calculation *process* readily generalizes to any number of objects – say M, N, O, P – whose *cardinality* would equal **M x N x O x P.
**

When more than two objects are involved, the *process* earns a more cosmopolitan designation – ** Tensor Product’**.