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) )

--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: A noiseless patient Spider (3:633/280.2@fidonet)

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--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: A noiseless patient Spider (3:633/280.2@fidonet)

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

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

Python says:ÿ (1 Combination 2) = 0

ÿÿÿÿÿÿÿÿ Ok... It's Impossible (to do).

ÿÿÿÿÿÿÿÿÿÿÿÿÿ ------- is there a Better explanation?



(5 Combination 0) = 1ÿ <---- This is explained byÿ Comb(5,0)=Comb(5,5)

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ in general:ÿÿ Comb(N,r)=Comb(N,N-r)

_______________________________________

from math import comb

for i in range(6):ÿÿÿÿÿ print( comb(5,i) )

print( comb(1,2)ÿ )

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!ÿ 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


--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: A noiseless patient Spider (3:633/280.2@fidonet)

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--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: A noiseless patient Spider (3:633/280.2@fidonet)

HenHanna <HenHanna@devnull.tb> writes:

Python says: (1 Combination 2) = 0
Ok... It's Impossible (to do).
------- is there a Better explanation?

JB has given you an explanation to do with generalising the algebraic equations, but there are also simple explanations from first principles.

(5 Combination 0) = 1 <---- This is explained by Comb(5,0)=Comb(5,5)
in general: Comb(N,r)=Comb(N,N-r)

I'll write |[5,0]| for this. In general |[n,m]| is the number of
m-element subsets of a typical set of n elements. So how many
zero-element subsets of such a set are there? Just 1. |[n,0]| = 1.

And how many 2-element subsets of a 1-element set are there? 0, so
|[1,2]| = 0.

--
Ben.

--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: A noiseless patient Spider (3:633/280.2@fidonet)