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From: HenHanna <HenHanna@devnull.tb>
Newsgroups: comp.lang.python,sci.math,sci.lang
Subject: Re: (1 Combination 2) = 0 -- Better explanation?
Date: Mon, 15 Jul 2024 11:49:39 -0700
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On 7/14/2024 8:44 PM, Jeff Barnett wrote:
> On 7/14/2024 2:57 PM, HenHanna wrote:
>>
>> Python says:  (1 Combination 2) = 0
>>
>>          Ok... It's Impossible (to do).
>>
>>               ------- is there a Better explanation?
>>
>>
>>
>> (5 Combination 0) = 1  <---- This is explained by  Comb(5,0)=Comb(5,5)
>>
>>                                       in general:   Comb(N,r)=Comb(N,N-r)
>>
>> _______________________________________
>>
>> from math import comb
>>
>> for i in range(6):      print( comb(5,i) )
>>
>> 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