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Posers and Puzzles

Posers and Puzzles

  1. Standard member 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>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. Standard member 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. Standard member 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. Standard member 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. Standard member 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 07:54 / 2 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. Standard member 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 "prove that 0!=0"?
  9. Donation Acolyte
    Now With Added BA
    24 Jun '04 15:53 / 1 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. Standard member 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. Standard member 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. Standard member 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. Standard member genius
    Wayward Soul
    07 Sep '05 12:22
    Originally posted by Bowmann
    Yep.
    ?