# 0!

genius
Posers and Puzzles 20 Jun '04 21:32
1. genius
Wayward Soul
20 Jun '04 21:32
0!=1!=!, and the question to you is...why?! (! is factorial, i.e. teh product of all the numbers up to that nubmer, like 5!=1*2*3*4*5 - but you all knew that, didn't you?)
2. 20 Jun '04 21:46
n! is defined as follows:
0!=1
for n&gt;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
3. genius
Wayward Soul
20 Jun '04 21:51
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
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?
4. royalchicken
CHAOS GHOST!!!
21 Jun '04 01:09
You'll just get x*lnx - x plus a constant. How about do it other than a simple way though.

Genius's modified puzzle:

Integrate ln x in the most convoluted way possible...
5. TheMaster37
Kupikupopo!
21 Jun '04 17:57
Originally posted by genius
0!=1!=!, and the question to you is...why?! (! is factorial, i.e. teh product of all the numbers up to that nubmer, like 5!=1*2*3*4*5 - but you all knew that, didn't you?)
I love this argument for 0!

0! = 1! /1 = 1/1 = 1
6. royalchicken
CHAOS GHOST!!!
23 Jun '04 02:54
Why not just define k! as the number of permutations of k objects? If you have zero objects, then you have one possible permutation, so 0! = 1 with no special case definition.
7. 24 Jun '04 07:542 edits
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.
8. genius
Wayward Soul
24 Jun '04 15:23
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.
well-how about &quot;prove that 0!=0&quot;? ðŸ˜›
9. Acolyte
24 Jun '04 15:531 edit
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.
Even sillier is the following definition: n! := Gamma(n+1)
10. opsoccergurl11
rockin soccer kid
24 Jun '04 16:46
i 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.
11. opsoccergurl11
rockin soccer kid
24 Jun '04 16:51
by the way, im gonna be a freshman in highschool (but im in advanced math), so if that doesnt make any sense, its my fault, not urs.
12. Bowmann
Non-Subscriber
06 Sep '05 17:42
Originally posted by royalchicken
Why not just define k! as the number of permutations of k objects? If you have zero objects, then you have one possible permutation, so 0! = 1 with no special case definition.
Yep.
13. genius
Wayward Soul
07 Sep '05 12:22
Originally posted by Bowmann
Yep.
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