In article <XWIfk.15144$4A6.12587@[EMAIL PROTECTED]
>, Jack <jj@[EMAIL PROTECTED]
>
wrote:
> "Paul Sperry" <plsperry@[EMAIL PROTECTED]
> wrote in message
> news:160720082107587503%plsperry@[EMAIL PROTECTED]
> > In article <Mksfk.20$dl5.11@[EMAIL PROTECTED]
>, Jack <jj@[EMAIL PROTECTED]
>
wrote:
> >
> >> Paul,
> >>
> >> One chief reason why it looks right that, in my notation, I
retain
> >> the
> >> full x,y in eg. N(x,y,t_j) instead of using only x is that on
occasions I
> >> replace x and y with specific prescribed values.
> >
> > I presume x and y come from [x, y]. Since you now say y - x is
> > variable, y is not determined by x, so it appears you _must_ include
y.
>
> But if I always begin every proof of every proposition that I lay down,
with
> 'given x,y', then surely it's as good as saying something like 'given
x=1',
> in which case y is the only variable necessary to reference. I can see
your
> point, though, if I am not insisting on a *specific* [x,y] throughout.
There is a _big_ difference between talking about any old interval,
[x,y], and intervals of the form [1,y].
The phrase "given x, y" is not some magical incantation; it merely
serves notice that you are going to be talking about x and y.
Things like this are why I've been urging you to start at the beginning
and go to the end. I want you to go A to B to C to .... _You_ want to
go E to A to W back to A to Y...
> > I'm guessing N(x,y,t) is some sort of function - it is probably a
> > surrogate for N([x,y],t). In any case, if it is a function, you are
> > obliged to give its domain and codomain; i.e. N : ? -> ??.
>
> It's sum{t(n), n : n in [x,y]}.
That's nice - or it would be if you deleted the comma after "t(n)" and
the "n" after the comma. However, it does not answer the question. To
be a function N must have a domain and a codomain. That is N : A -> B;
N turns _all_ elements in A (and only those) into elements of B. In
this case I guess B = |N. What is A? What is the _totality_ of things I
am allowed to "plug into" N? Notice the "totality"; you must be able to
describe every single thing that x can be, that y can be and that t can
be.
> Incidentally, I am thinking of replacing some of my variables with sets,
and
> referencing their cardinality to replace my original reference to the
> variable. I can see one sole advantage in that it does away with the
need to
> define an extra set quite a bit later on in my paper, albeit one that I
> thought looked a congenial creation, it being a set A that was placed in
> contradistinction to a set B. Would you say it's advisable to use avoid
> defining sets, in favour of defining variables, where possible?
I have no idea; I'd have to see what led up to that.
--
Paul Sperry
Columbia, SC (USA)
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