In article <MZ9ek.167569$8H5.31103@[EMAIL PROTECTED]
>, Jack
<jj@[EMAIL PROTECTED]
> wrote:
> Paul,
>
> > So you want something like
> >
> > "If f : |N -> |N , let c_f(n) = (1/2)*f(n)*(f(n) - 1)"
> >
> > Since c depends on the function it must be tagged somehow with the
> > function name.
> >
> > You can then continue:
> >
> > "Let J be a set of primes and for n in |N define
> > t(n) = |{p in J : p divides n}|".
> >
> > Then you can refer to c_t(n) if needs be.
>
> I don't quite know whether your reply answers the issue I have here, but
my
> problem is not writing out the definition of t(n) for which t(n) is
> determined by the divisibility on n. I've got that done already.
Yes, I know, but your notation has not settled down yet.
> It's
> writing out the definition of t: N ---> N is arbitrary, and my not
knowing
> whether the change in definition of t(n) will mean that anything needs
to be
> said as regards c(n), which after the second definition is laid down
becomes
> c(n,J).
You can't do that; c and c(-,J) are two different things. What you
_can_ do is call your "count the divisors" function t_J and then
_define_ c(n, J) = c_(t_j)(n). In fact that wouldn't be a bad idea
since subscripted subscripts are to be avoided if possible.
Previously, referring to "arbitrary" t and "count the divisors" t you
wrote "But I want c(n) to be (t(n)(t(n)-1))/2 for both cases." That led
me to believe that you wanted c to be defined by the indicated
expression no matter what the function t was.
Let me emphasize since c_f _does_ depend on f it must be tagged somehow
with f. You seem to be reluctant to do that and it is going to cause
you problems - like using "t" for two different functions.
When I wrote "If f : |N -> |N , let c_f(n) = (1/2)*f(n)*(f(n) - 1)" I
was saying that, no matter what the function is, c_f is defined the way
you indicated. Since I said nothing about f except that it was a
function from |N to |N that _automatically_ makes it "arbitrary".
What do you think "arbitrary" means? I'm not being snotty; it seems you
are reading more into it than there is. It is rarely necessary or
desirable to say something is "arbitrary". If I say let g : |N ->|N and
nothing else, g is "arbitrary". If I say h : |N -> |N and h(4) = 0 then
h is _not_ arbitrary.
--
Paul Sperry
Columbia, SC (USA)
|
