three binomial(n,k) definitions

[Brendan McKay]

* Michael Somos <somos at grail.cba.csuohio.edu> [021215 05:52]:
> seqfan,
> 
>       Brendan McKay writes that :
> 
> > is adopted.  The reason is that the BINOMIAL THEOREM
> > requires
> >    binomial(n,k) = n*(n-1)*...*(n-k+1) / k!
> > for all non-negative integers k, REGARDLESS of n and even
> > if n is a complex number!  Vast tracts of mathematics,
> 
> and is perhaps overstating his case for dramatic emphasis.

No, I was serious and even forgot to mention dogs biting their
owners and widespread crop failures.

Some consistency in mathematical terminology is important and
people who try to undermine standards as deeply entrenched as
the definition of binomial(n,k) for positive integer k are
working for the Forces of Evil.  I'm not saying you aren't
allowed to play with nonstandard ways to extend the triangle
0 <= k <= n to other n; I'm saying you can't refer to the result
as binomial(n,k) without being WRONG.

Brendan.