XPost: sci.math, sci.lang

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) )

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.math, sci.lang

T24gNy8xNC8yMDI0IDI6NTcgUE0sIEhlbkhhbm5hIHdyb3RlOg0KPiANCj4gUHl0aG9uIHNh eXM6wqAgKDEgQ29tYmluYXRpb24gMikgPSAwDQo+IA0KPiAgwqDCoMKgwqDCoMKgwqAgT2su Li4gSXQncyBJbXBvc3NpYmxlICh0byBkbykuDQo+IA0KPiAgwqDCoMKgwqDCoMKgwqDCoMKg wqDCoMKgIC0tLS0tLS0gaXMgdGhlcmUgYSBCZXR0ZXIgZXhwbGFuYXRpb24/DQo+IA0KPiAN Cj4gDQo+ICg1IENvbWJpbmF0aW9uIDApID0gMcKgIDwtLS0tIFRoaXMgaXMgZXhwbGFpbmVk IGJ5wqAgQ29tYig1LDApPUNvbWIoNSw1KQ0KPiANCj4gIMKgwqDCoMKgwqDCoMKgwqDCoMKg wqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoCBp biBnZW5lcmFsOsKgwqAgQ29tYihOLHIpPUNvbWIoTixOLXIpDQo+IA0KPiBfX19fX19fX19f X19fX19fX19fX19fX19fX19fX19fX19fX19fX18NCj4gDQo+IGZyb20gbWF0aCBpbXBvcnQg Y29tYg0KPiANCj4gZm9yIGkgaW4gcmFuZ2UoNik6wqDCoMKgwqDCoCBwcmludCggY29tYig1 LGkpICkNCj4gDQo+IHByaW50KCBjb21iKDEsMinCoCApDQoNCkxldCBjb21iaW5hdGlvbiBv ZiBuIHRoaW5ncyB0YWtlbiBtIGF0IGEgdGltZSBiZSByZXByZXNlbnRlZCBieSBbbixtXS4g DQpUaGVuIFtuLG1dID0gW24sbi1tXSBhcyB5b3UgY29ycmVjdGx5IG5vdGUgYWJvdmUuIEZ1 cnRoZXIsIHdlIGhhdmUgdGhlIA0KY29tcHV0YXRpb25hbCBmb3JtdWxhIFtuLG1dID0gbiEv KG0hKG4tbSkhKSB3aGVyZSB4ISAgaXMgc2ltcGx5IHggDQpmYWN0b3JpYWwuIFNvIFsxLDJd ID0gMSEvKDIhKCgtMSkhKSksIG9yIDEvMiBkaXZpZGVkIGJ5ICgtMSkhLiBIb3dldmVyIA0K ZmFjdG9yaWFsIG9mIGEgbmVnYXRpdmUgaW50ZWdlciBpcywgYnkgY29udmVudGlvbiwgYW4g aW5maW5pdGUgdmFsdWUgc28gDQpbMS4yXSA9IDAuDQotLSANCkplZmYgQmFybmV0dA0KDQo=

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.math, sci.lang

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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.math, sci.lang

T24gNy8xNS8yMDI0IDEyOjQ5IFBNLCBIZW5IYW5uYSB3cm90ZToNCj4gDQo+IE9uIDcvMTQv MjAyNCA4OjQ0IFBNLCBKZWZmIEJhcm5ldHQgd3JvdGU6DQo+PiBPbiA3LzE0LzIwMjQgMjo1 NyBQTSwgSGVuSGFubmEgd3JvdGU6DQo+Pj4NCj4+PiBQeXRob24gc2F5czrCoCAoMSBDb21i aW5hdGlvbiAyKSA9IDANCj4+Pg0KPj4+IMKgwqDCoMKgwqDCoMKgwqAgT2suLi4gSXQncyBJ bXBvc3NpYmxlICh0byBkbykuDQo+Pj4NCj4+PiDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDC oCAtLS0tLS0tIGlzIHRoZXJlIGEgQmV0dGVyIGV4cGxhbmF0aW9uPw0KPj4+DQo+Pj4NCj4+ Pg0KPj4+ICg1IENvbWJpbmF0aW9uIDApID0gMcKgIDwtLS0tIFRoaXMgaXMgZXhwbGFpbmVk IGJ5wqAgQ29tYig1LDApPUNvbWIoNSw1KQ0KPj4+DQo+Pj4gwqDCoMKgwqDCoMKgwqDCoMKg wqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKg wqAgaW4gZ2VuZXJhbDogICANCj4+PiBDb21iKE4scik9Q29tYihOLE4tcikNCj4+Pg0KPj4+ IF9fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fXw0KPj4+DQo+Pj4gZnJv bSBtYXRoIGltcG9ydCBjb21iDQo+Pj4NCj4+PiBmb3IgaSBpbiByYW5nZSg2KTrCoMKgwqDC oMKgIHByaW50KCBjb21iKDUsaSkgKQ0KPj4+DQo+Pj4gcHJpbnQoIGNvbWIoMSwyKcKgICkN Cj4gDQo+IA0KPj4NCj4+IExldCBjb21iaW5hdGlvbiBvZiBuIHRoaW5ncyB0YWtlbiBtIGF0 IGEgdGltZSBiZSByZXByZXNlbnRlZCBieSBbbixtXS4gDQo+PiBUaGVuIFtuLG1dID0gW24s bi1tXSBhcyB5b3UgY29ycmVjdGx5IG5vdGUgYWJvdmUuIEZ1cnRoZXIsIHdlIGhhdmUgdGhl IA0KPj4gY29tcHV0YXRpb25hbCBmb3JtdWxhIFtuLG1dID0gbiEvKG0hKG4tbSkhKSB3aGVy ZSB4IcKgIGlzIHNpbXBseSB4IA0KPj4gZmFjdG9yaWFsLiBTbyBbMSwyXSA9IDEhLygyISgo LTEpISkpLCBvciAxLzIgZGl2aWRlZCBieSAoLTEpIS4gSG93ZXZlciANCj4+IGZhY3Rvcmlh bCBvZiBhIG5lZ2F0aXZlIGludGVnZXIgaXMsIGJ5IGNvbnZlbnRpb24sIGFuIGluZmluaXRl IHZhbHVlIA0KPj4gc28gWzEuMl0gPSAwLg0KPiANCj4gDQo+IFRIYW5rIHlvdS4uLg0KPiAN Cj4gDQo+ICDCoEJhcmQuR29vZ2xlLmNvbcKgwqAgc2F5cyB0aGF0DQo+IA0KPiAgwqDCoMKg wqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqAgQ29tYigxLDIpIGlzIG5vdCBkZWZp bmVkDQo+IA0KPiAgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgIGZhY3RvcmlhbCgt MSkgaXMgbm90IGRlZmluZWQNCj4gIMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoMKgwqDCoCBm YWN0b3JpYWwoLTIpIGlzIG5vdCBkZWZpbmVkDQo+IA0KPiAgwqDCoMKgwqDCoMKgwqDCoMKg wqDCoCBHYW1tYUZ1bmN0aW9uKC0xKSBpcyBub3QgZGVmaW5lZA0KPiAgwqDCoMKgwqDCoMKg wqDCoMKgwqDCoCBHYW1tYUZ1bmN0aW9uKC0yKSBpcyBub3QgZGVmaW5lZA0KPiANCg0KVGhl eSBhcmUgcGFydGlhbGx5IGNvcnJlY3QuIEhvd2V2ZXIsIG9uZSBjYW4gc2F5IHRoYXQgMS8w ID0gb28gaXMgDQpkZWZpbmVkICh3aGVyZSBvbyBpcyBpbmZpbml0eSkuIEluIHBhcnRpY3Vs YXIuIDEvb28gPSAwIGNlcnRhaW5seSBtYWtlcyANCnNlbnNlIGFuZCB0aGF0J3MgYWxsIHdl ICBuZWVkIHRvIGFjY2VwdCBmb3IgdGhlIGFib3ZlIGRlZHVjdGlvbnMuDQoNClNvbWV0aGlu ZyBJIGZvcmdvdCB0byBzYXkgaW4gbXkgb3JpZ2luYWwgYWJvdmUgaXMgd2h5IHghID0gb28g d2hlbiB4IGlzIA0KYSBuZWdhdGl2ZSBpbnRlZ2VyLiBJIGN1cmUgdGhhdCBvbWlzc2lvbiBu b3cuIFdlIHdhbnQgdG8gZGVmaW5lIHRoZSANCmZhY3RvcmlhbCBhcyAxISA9IDEgYW5kIG4h ID0gbioobi0xKSEgd2hlbiBuID4gMS4gV2Ugd291bGQgYWxzbyBsaWtlIHRvIA0KYmUgYWJs ZSB0byBwZWRhbCBiYWNrd2FyZHMsIGkuZS4uIGRlcml2ZSAobi0xKSEgZnJvbSBuISBhbmQg bi4gVGhpcyBpcyANCmNlcnRhaW5seSBzdHJhaWdodGZvcndhcmQgd2hlbiBuID4gMC4gSG93 ZXZlciB0aGUgY2FzZXMgZm9yIG90aGVyIA0KaW50ZWdlciBuIGlzIHRyaWNraWVyLiBGb3Ig ZXhhbXBsZSwgZnJvbSBvdXIgcmVjdXJzaW9uIGZvcm11bGEgd2UgaGF2ZSANCjAhID0gMCoo LTEpISBhbmQgd2Uga25vdyB0aGF0IChieSBkZWZpbml0aW9uKSAwISA9MS4gVGh1cywgMSA9 IDAqKC0xKSEgDQp3aGljaCBvbmx5IGhhcyB0aGUgcG9zc2libGUgc3ltYm9saWMgc29sdXRp b25zICgtMSkhID0gb28gb3IgLW9vLiBOb3cgYSANCnRyaXZpYWwgaW5kdWN0aW9uIGFyZ3Vt ZW50IHdpbGwgZHJhdyB0aGUgc2FtZSBjb25jbHVzaW9uIGZvciBhbGwgDQpuZWdhdGl2ZSBp bnRlZ2Vycy4NCg0KVGhlIGltcG9ydGFuY2Ugb2YgdGhpcyBiaXQgb2Ygc29waGlzdHJ5IGlz IG91ciBkZXNpcmUgdG8gZG8gc3ltYm9saWMgDQptYW5pcHVsYXRpb25zIHdpdGggdmFyaW91 cyBjbGFzc2VzIG9mIGZvcm11bGFzIHdpdGhvdXQgaGF2aW5nIHRvIA0KbnVtZXJpY2FsbHkg c2VwYXJhdGUgb3V0IGEgbG90IG9mIHNwZWNpYWwgY2FzZXMuIExvb2sgYXQgdGhlIGFib3Zl IA0KZGVmaW5pdGlvbiBvZiBjb21iaW5hdGlvbi4gV2l0aCB0aGUgZXN0YWJsaXNoZWQgY29u dmVudGlvbnMsIHdlIGhhdmUgMSkgDQpbbixuXSA9IDEgYW5kIHRoaXMgY2FuJ3Qgd29yayB1 bmxlc3MgMCEgPSAxOyAyKSBbbi4wXSA9IDEgd2hpY2ggc2F5cyANCnRoYXQgdGhlIG9ubHkg byBlbGVtZW50IHN1YnNldCBvZiBuIGVsZW1lbnRzIGlzIHRoZSBlbXB0eSBzZXQ7IGV0Yy4N Cg0KSXQgaXMgYSBnb2FsIG9mIG1hdGhlbWF0aWNpYW5zIHRvIG1ha2UgdGhlaXIgZGVmaW5p dGlvbnMgd29yayBub3Qgb25seSANCmZvciB0aGUgb2J2aW91cyBjYXNlcyBidXQgd2hlcmUg dGhlcmUgaXMgZGFya25lc3MgaW4gb3VyIGtub3dsZWRnZSB0aGF0IA0KbWlnaHQgYmUgdHJp dmlhbGx5IGlsbHVtaW5hdGVkIGJ5IGZvcm11bGFzIHRoYXQgYWxsb3cgc3RyYWlnaHRmb3J3 YXJkIA0KY29uc2lzdGVudCB0cmVhdG1lbnQgdGhyb3VnaG91dC4NCi0tIA0KSmVmZiBCYXJu ZXR0DQoNCg==

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.math, sci.lang

HenHanna <[email protected]> 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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)