Paul,
>> So maybe it would be N(x, y, t) for the arbitrary case and N(x, y,
>> t_{J}(n))
>> for the non-arbitrary?
>
> Well, close anyway. Here's what I would do:
> For interval {a, a + 1, ..., a + d} and function f : |N -> |N define
> N(a,f) = sum(f(n) : n = a, ..., a + d). That would be the _general_
> case. For the particular case using t_J I would, without comment, write
> N(a, t_J).
>
I take it that for me it would then be N(x,t) and N(x,t_J) (possibly I
should substitute "x" for "x,y"; more on that later!).
And I suppose I could do the same for all other definitions that are
likewise dependent on t; so it would be c(n,t) and c(n,t_J) etc., all
without comment?
Incidentally, I am confused as to why, a couple of posts back, you
questioned the necessity of the definition c(n,t). I certainly need to
work
with it, and (1/2)t(n)(t(n)-1) is surely unwieldy..
Also, as yet I have laid down a definition of c(n,t) and, *also*, of an
expression that will in my new notation be c(x,t) (or perhaps c(x,y,t).
The
second of these is the sum of c(n,t) over [x,y]. I take that the second
definition *is* necessary? I guess c(x,t) could mean anything; but perhaps
you'll advise me to use a completely different term to denote it.
>
> When you are working with functions, please think of Bob.
> You could write N(x,y,Bob) but not N(x,y,Bob(2)) or even N(x,y,Bob(n)).
>
Useful to know - thanks.
>> If OK, how would I write out my initial definition/function?
>>
>>
>> >
>> >> in a given interval [x,y];
>> >
>> > _over_ [x, y]. (If you still have all intervals of the same length,
you
>> > would be doing everybody a favor if you dropped the redundant "y".)
>>
>> Good thought.
>
> 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. I lay down every
proposition
beginning "given x,y.", or "for all x,y"; furthermore, my worry is that if
I
make a reference only to x, such as with c(x,t), then it might appear that
I
am only interested in x, as though I am considering it as a value n and
that
it can be written as c(n,t) for which n=x.
Incidentally, I wonder whether you could advise me on the use of "for
integers n over [x,y]" in relation to the use of "for integers n *in*
[x,y]"..?
In particular I am wavering in the phrase ".for each of at least |J|
values
of n over [x,y]."
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"..
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)". I have defined a set specifically for it,
and
reference it in the expression; but I don't use it for anything else and I
would rather not have it cluttering my paper. If there's a better way of
writing it.?
With many thanks.
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