Here's the official definition:

Where n cannot be a decimal or a fraction
or a radical or a negative number... 
n must be a whole number.

* 0! is specifically defined to be 1...

(If it isn't, our formulas in the next sections won't work!)

Yes, you have the button on your calculator, but, I'd like you to get comfortable working with these WITHOUT your calculator.  Why?

Try popping 70! into your calculator.

That probably gave you an error...  If it didn't, try 450!  THAT should definitely be a problem!

On regular calculators, 69! is the biggest thing it can handle -- on graphing calculators, it's 449!

So, we need to learn to live without our calculators!