N Factorial (N!) Calculator
A Science Program by Jay Tanner - 2020
This program computes the EXACT value for any
non-negative integer argument from 0 to 9999.

Enter N (0  to  9999)      

The EXACT value of 0! (factorial) is shown below and consists of 1 digit.

Double-Click to Select ALL Text

Because factorials can become extremely large very quickly, the program is limited to 9999 as the maximum argument value because, depending on the server computer, it could take up to several seconds to compute very large factorial values and the program could possibly time-out if taking too long to complete a computation.

In Permutations, Nothing Counts as Something
If the factorial of non-negative integer N simply equates to the product all of the integers from 1 up to N multiplied together, then why does the factorial of 0 (zero) equate to 1?

The reason zero factorial equates to 1 is essentially due to its physical definition.  There is always the 1 possibility of there being nothing at all.

Physically, the value of the factorial represents a count of the total number of distinct ways that N distinct entities can be arranged in a row.  There is only 1 physical way that 0 (zero) entities can be arranged in a row, and even though it equates to an empty set, and essentially a moot point, it still counts as 1.  Like an empty box, the set exists, but there is nothing in it.

A PHP Science Program by Jay Tanner - 2020