Here are two familiar mathematical abbreviations:

And a new one:

4! (4 factorial) has a value of 24. In general, n! is the product of all the numbers up to n. Factorial operations rear their head in unexpected places, but for all their novelty, their behavior is pretty simple. Each factorial has a simple relation to the one below it:

Because:

Similarly,

And:

And so on.

It's also simple to see that:

Since 5! = 5 × 4!. And, obviously:

These principles will be put to use in the next section, in which all the elements presented so far come together at last.