In article <FF8ek.131713$AH5.119809@[EMAIL PROTECTED]
>, Jack
<jj@[EMAIL PROTECTED]
> wrote:
> Paul,
>
> >
> > You already know this is going to get you in trouble.
> >
> >>the first I fix with the definition 'let t : N ---> N be arbitrary'.
> >
> > This isn't a definition and you can't "fix" an arbitrary function.
> >
>
> I used the word fix in the belief that it means ' take it to be
> such-and-such until further notice'.
>
> >>Immediately after the first definition, I define c(n) as
> >>(t(n)(t(n)-1))/2.
> >
> > This is a problem since your first "definition" didn't define anything
> > so c(n) could be virtually any number.
> >
>
>
> I don't mind as long as t(n) is a finite integer.
>
>
> > I think the first "definition" was in regard to the _letter_ "t" and
it
> > was supposed to say that the letter "t" was going to stand for a
> > function from |N to |N.
> >
> > Here is what I think you meant:
> >
> > "Let J be a set of primes and for n in |N define
> > t(n) = |{p in J : p divides n}| and let c(n) = (1/2)*t(n)*(t(n) - 1)."
> >
>
> That's more like my second definition. The first doesn't have anything
to do
> with primes. But I want c(n) to be (t(n)(t(n)-1))/2 for both cases.
>
> With thanks.
>
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.
BTW, you can't depend on me remembering anything that was said in
previous threads.
You may want t_J instead of t - I don't know.
--
Paul Sperry
Columbia, SC (USA)
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