O Plameras wrote:
Another way of saying: factorial 0 = 1 is a "by definition" thing in Mathematics and everybody then accepts it,
factorial(0) = 1 makes sense, because factorials are a measure of the number of ways you can combine items. 1! = 1 way to arrange one item (a) 2! = 2 ways to arrange two items (a b), (b a) 3! = 6 ways to arrange three items (a b c) (a c b) (b a c) (b c a) (c a b) (c b a) So how many different ways can you arrange the empty set ()? One. It cannot be zero, as this implies the empty set cannot be a set (ie, you've defined the empty set out of existence, which in turn implies no zero (as it is the count of items of the empty set), and your arithmetic quickly losses usefulness as operations such as subtraction become undefined). It's often the way with edge cases that we choose the case that leaves our arithmetic with the most power. [ This isn't to say there aren't good uses for limited arithmetics with slightly differing rules (eg, in computing it's often convenient to see if ADD can be substituted with XOR and if the arithmetic properties we need are retained). ] It's also trivial to show factorial(n-1) <= factorial(n). So there cannot be greater than one ways to arrange the empty set. -- Glen Turner Tel: (08) 8303 3936 or +61 8 8303 3936 Australia's Academic & Research Network www.aarnet.edu.au -- SLUG - Sydney Linux User's Group Mailing List - http://slug.org.au/ Subscription info and FAQs: http://slug.org.au/faq/mailinglists.html
