by "Jack" <jj@[EMAIL PROTECTED]
>
Jul 12, 2008 at 09:41 PM
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.
