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'.
>> <<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).
>> 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. 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.
>> Then, I want a set of sets S(n',n'), S(n,n') being a set comprising
>> t(n')-t(n) members (each member being an occupied matrix component),
such
>> that (n,n') is in [x,y]x[x',y'] but neither n nor n' are members of a
>> pair
>> R(n,n'), and t(n')-t(n) >1.
>
> Wow - I'm mystified. 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?
> The waters, in regard to matrices and arrays, could hardly be muddier.
> I haven't a clue as to what you are trying to do. Since, as near as I
> can tell, what you have done so far involves a set of primes and two
> intervals, you should be able to do the calculations in this very
> specific case so that I (and maybe you) would have a better idea of
> what is going on.
>
> I'll go farther: if you can't calculate, for a particular small
> example, everything you've talked about so far then you've got serious
> problems.
Sorry, but I just didn't know exactly what you were asking; I didn't know
what was meant by the references "[2,7] and [5,10]" nor exactly what you
wanted exemplified.
With thanks.
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