Results 1 to 10 of 10

Math Help - wikipedia entry on Pascal's rule

  1. #1
    Member
    Joined
    Oct 2010
    From
    Mumbai, India
    Posts
    203

    wikipedia entry on Pascal's rule

    Hi

    here is link to Pascal's rule at wikipedia

    Pascal's rule - Wikipedia, the free encyclopedia

    its written as

    \binom{n}{k}+\binom{n}{k-1}=\binom{n+1}{k} \;\mbox{for}\;1\le k\le n+1

    if we plug in k=n+1 , we get

    \binom{n}{n+1}+\binom{n}{n}=\binom{n+1}{n+1}

    \Rightarrow  \binom{n}{n+1}=0


    is something wrong ?

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2010
    From
    Mumbai, India
    Posts
    203

    Re: wikipedia entry on Pascal's rule

    i think the range should defined as

    1\le k\le n

    right ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: wikipedia entry on Pascal's rule

    Quote Originally Posted by issacnewton View Post
    i think the range should defined as

    1\le k\le n

    right ?
    How would you define

     \binom{n}{n+1}?

    It seems to involve (-1)! in the denominator which I'm sure Pascal would not approce of.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2010
    From
    Mumbai, India
    Posts
    203

    Re: wikipedia entry on Pascal's rule

    thats what i was wondering.. is wikipedia entry wrong then ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: wikipedia entry on Pascal's rule

    Quote Originally Posted by issacnewton View Post
    thats what i was wondering.. is wikipedia entry wrong then ?
    I beleive so, >>Planet Math's<< limits for k are what we might expect

    I think I should also give >>Proof Wiki's<< page a plug.

    CB
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2010
    From
    Mumbai, India
    Posts
    203

    Re: wikipedia entry on Pascal's rule

    Thanks captain , So did you fix 'proof wiki' page. When I went there, it was ok. Ask somebody at wikipedia to fix it.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: wikipedia entry on Pascal's rule

    Quote Originally Posted by issacnewton View Post
    Thanks captain , So did you fix 'proof wiki' page. When I went there, it was ok. Ask somebody at wikipedia to fix it.
    Proof Wiki is nothing to do with Wikipedia, it is a site maintained by a sometime helper here on MHF.

    CB
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: wikipedia entry on Pascal's rule

    Some authors define
    \binom{n}{k}=0
    whenever it is not true that 0 \leq k < n.

    See, for example, Knuth, "The Art of Computer Programming, Vol 1", or
    Binomial Coefficient -- from Wolfram MathWorld.

    By this definition, it is correct to say that
    \binom{n}{n+1} = 0.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Oct 2010
    From
    Mumbai, India
    Posts
    203

    Re: wikipedia entry on Pascal's rule

    if that is what the definition is , then all is well............
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: wikipedia entry on Pascal's rule

    Quote Originally Posted by issacnewton View Post
    if that is what the definition is , then all is well............

    It is not the definition but a definition. Knuth is particularly known for this sort of thing (defining undefined notation in a manner which suits his current purpose), but it is also consistent with interpretation of the factorial in terms of the gamma function.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. exponential function on wikipedia
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 5th 2011, 11:03 AM
  2. Pascal's Rule
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: July 6th 2010, 11:34 AM
  3. Accounting - Journal Entry
    Posted in the Business Math Forum
    Replies: 1
    Last Post: May 11th 2010, 06:56 PM
  4. Entry Level Mathematics
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: August 4th 2008, 01:30 AM

/mathhelpforum @mathhelpforum