In article <J8TXj.19960$sv3.3291@[EMAIL PROTECTED]
>, Jack <jj@[EMAIL PROTECTED]
>
wrote:
> Paul,
>
> > See <http://en.wikipedia.org/wiki/Matrix_%28mathematics%29>;
scroll
> > down a little to the mathematical definition (you'll also see the
cross
> > product there).
> > See also <http://mathworld.wolfram.com/Array.html>.
> > You'll see why I am having so much trouble understanding what you are
> > getting at - the two references are speaking my language;
unfortunately
> > you aren't.
>
> The mathworld reference had this:
>
> "Square Array ( Wolfram MathWorld )
> An n×n array is called a square array. Considered as a matrix, a square
> array is called a square matrix."
>
> I don't see how I'm so far off, nor why you said previously that the
term
> array is not strictly a mathematical term. Perhaps I should have said a
> 'rectangular array'.
Actually, I said that "array" was not a _common_ mathematical term. You
will have noticed that Wollfram was talking about a Mathematica
command.
From the start, you have distinguished between matrices and arrays but
you have never been willing to tell me what you thought an array _was_.
Some time ago I suggested a "list of lists" in then manner of Wollfram
or programming in general. Here it is again:
"Here's an example - the numbers have nothing to do with your problem.
It is sort of suggested by your mention of "histogram".
A := [U, V, W, X]
U := [1, 2, 3]
V := [4, 5, 6, 7]
W := [8, 9]
X := [ 10, 11, 12]
A is an array (of arrays); U, V, W and X are arrays.
A[0] = U; A[2] = W; A[2][1] = A[2, 1] = W[1] = 9.
Schematically (row dominant) A is
1 2 3
4 5 6 7
8 9
10 11 12"
> >> <<You could then Let R = {R(n,n') : (n,n') in K}.Then you could add
up or
> >> minimize the elements of R. Equivalently you could form
> >> sum(R(n,n') : (n,n') in K) or min(R(n,n') : (n,n') in K).>>
> >>
> >> This looks to be the kind of thing I am after. I want the minimum
> >> possible
> >> value of sum_#R(n,n'),
> >
> > This isn't at all clear; sum(R(n,n') : (n,n') in K) is just a number.
>
>
> What's the problem with that? BTW note I write sum_#R(n,n'); each value
of
> #R(n,n') is t(n,m)-t(n',m).
Frankly, I thought that was a typo. I guessed you were using the pound
sign to indicate the size of a set. But "sum_#R(n,n')" says literally
the word "sum" subcripted by the size of R(n,n').
> >> and a set of sets R(n,n') so that I have got a set
> >> comprising every (n,n') for which there is a value #R(n,n').
> >
> > Saying #R(n,n') is like saying #2.
>
>
> But all along I have been trying to ask for help defining R(n,n') as a
set,
> not just as a number.
But you _said_ "R(n,n') = t(n,m)-t(n',m)" which gives R(n,n') as a
single number. How am I supposed to think that it is anything else?
> As I made clear, that was the reason I kept on with my
> arrays. I am trying to define #R(n,n') -- or, in other notation,
|R(n,n')|,
> presumably -- as a set of entries in a column (it doesn't matter exactly
> which ones, as long as they number t(n,m)-t(n',m)) and as you can see I
have
> been struggling. I hoped you might be able to help.
Lord knows I'm trying. The above paragraph is a pretty good example of
why I'm having so much trouble. You say you are trying to define the
size of the set R(n,n') even though you told me R(n,n') was a number.
You go on to tell me that the number of elements of R(n,n') is the
_set_ of entries in some column of something - that doesn't make any
sense. You wrap it up by apparently telling me that R(n,n') has t(n,m)
- t(n',m) elements - that pretty well decides the question of how many
elements R(n,n') has. Can you understand why I am puzzled and want an
example of all this?
If you want R(n,n') to be a set you are going to have to say what its
elements are. May some thing like the set of primes that divide n but
don't divide n' or something like that.
[...]
> > ... To answer one of your questions: it is not a good
> > idea to use both t(n) and t(n,P) even though context may make things
> > clear. Many of us consider "t" to be the name of the function so you
> > have two different functions with the same name.
> >
>
> What about something like t(n) and, for the other construct,
> t_{\alpha}(n,P), instead?
That would be OK - why not just a different letter?
[...]
--
Paul Sperry
Columbia, SC (USA)
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