- 20 Jun '04 21:51

don't you hate it when you post a puzzle that isn't so much a puzzle as a bit of knowledge that people'll get first time anyway? ah well-i've gotta find some more puzzle, or dig up some old uns...ah well-how about, for the mean time, integrate lnx?*Originally posted by Mouse2***n! is defined as follows:**

0!=1

for n>0, n!=n*(n-1)!

which is basically the same thing as teh product of all the numbers up to that nubmer, but it explains the 0 case - 24 Jun '04 15:23

well-how about "prove that 0!=0"?*Originally posted by piderman***I think those reasons are all made up after it was defined this way. That was probably because it fits best that 0!=1 and not that 0!=0, so people looked for 'logical' explanations. But that's the mathematicians way.** - 24 Jun '04 15:53 / 1 edit

Even sillier is the following definition: n! := Gamma(n+1)*Originally posted by piderman***I think those reasons are all made up after it was defined this way. That was probably because it fits best that 0!=1 and not that 0!=0, so people looked for 'logical' explanations. But that's the mathematicians way.** - 24 Jun '04 16:46i think another reason 0!=1 is because if you end up with a 0! in the denominator of a fraction, then the whole sentence becomes undefined. and sometimes the are solutions. like n choose r -

5 choose 0-

5!/(5-0)!*0!

there is one way to choose 0 out of 5, so it is possible. if 0!=0, then it would be undefined, whereas now it is 1.