In article <B2Kek.210220$312.49876@[EMAIL PROTECTED]
>, Jack
<jj@[EMAIL PROTECTED]
> wrote:
[...]
> > If all intervals are to have length d and you want the interval that
> > starts at x then for [x, y] you could use I_x as I have done
previously
> > or [x] or <x> (but not {x}).
> >
>
> They are not all the same length over my paper.
What!?? You surely don't mean that. I've asked previously and you said
they were of the same length. You have lead both Brian and I to believe
interval lengths were constant. My irate meter just went up a couple
notches.
I don't want to get tangled up in future notation. From what I
understand so far, you should start with something like this:
*******
Let |N be the set of non-negative integers.
Let I be a finite interval of integers.
DEFINITION 1. For a function t : |N -> N define
c_t(n) = (1/2)*t(n)*(t(n) - 1).
DEFINITION 2. For a set of primes J define t_J : |N -> |N by
t_J(n) = |{p in J : p divides n}|.
REMARK. For convenience of notation we will write c(J, n) instead of
c_(t_J)(n).
DEFINITION 3. For t : |N - |N define s_I(t) = sum(t(n) : n is in I);
define s'_I(t) = sum(t(n) : n is in I and t(n) > 1)
********
I suggest you take these or something very similar and go from there.
[...]
> In particular I am wavering in the phrase ".for each of at least |J|
values
> of n over [x,y]."
Should be "in".
> I get the feeling also that I might also need a bit of help in the use
of
> "for which" in preference to "such that"..
Probably doesn't matter provided the rest of the grammar is correct.
> One other cheeky question, if I may:
>
> I'm trying to say, in a part of one of my equations, "sum(t(n) over
[x,y]
> for all n for which t(n)>1)".
See DEFINITION 3.
--
Paul Sperry
Columbia, SC (USA)
|
