Re: (1 Combination 2) = 0 -- Better explanation?

On 7/14/2024 8:44 PM, Jeff Barnett wrote:

On 7/14/2024 2:57 PM, HenHanna wrote:

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Python says:  (1 Combination 2) = 0
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         Ok... It's Impossible (to do).
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              ------- is there a Better explanation?
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(5 Combination 0) = 1  <---- This is explained by  Comb(5,0)=Comb(5,5)
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                                      in general:   Comb(N,r)=Comb(N,N-r)
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from math import comb
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for i in range(6):      print( comb(5,i) )
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print( comb(1,2)  )

 Let combination of n things taken m at a time be represented by [n,m]. Then [n,m] = [n,n-m] as you correctly note above. Further, we have the computational formula [n,m] = n!/(m!(n-m)!) where x!  is simply x factorial. So [1,2] = 1!/(2!((-1)!)), or 1/2 divided by (-1)!. However factorial of a negative integer is, by convention, an infinite value so [1.2] = 0.

THank you...
  Bard.Google.com   says that
                     Comb(1,2) is not defined
                 factorial(-1) is not defined
                 factorial(-2) is not defined
             GammaFunction(-1) is not defined
             GammaFunction(-2) is not defined