While exploring factors in prealgbebra we would be amiss not to mention the simply delightful operator of factorials. Thus we find ourselves introducing the little magical operator who seems to work in his own little world of awesomeness. For one, the symbol for a factorial is the exclamation mark, ! , which just makes absolutely no sense. However, who doesn't want to know the secret behind this excitement? In fact, Paul Lockhart states in his book Arithmetic,
The main drawback (with the exclamation point) is that you have to restrain your enthusiasm when writing about numbers; if you write, "the answer is 5!" it might be confusing.
I'd say it is safe to say that with the choice of the exclamation mark, mathematicians became a little more droll. After all, we are now no longer to proclaim our excitement in the simple way that a philologist may. Tough times aside, what is a factorial?
A factorial is the product of the numbers from 1 to the given number. Thus, in our quote above, 5! (read 5 factorial) is actually, 5 x 4 x 3 x 2 x 1 =120 . These integers (prime and composite) have all come together to make (facere) a new number, 120. How cool is that? Did mathematicians just take this cool operator, define it, and leave it there? Absolutely not. In fact, the factorial was not invented but discovered as a necessary operation, but that's a tale for another day...