On Fri, 25 Apr 2008 18:26:42 +0100, Jack <jj@[EMAIL PROTECTED]
>
wrote in <news:mvoQj.60180$_h7.32264@[EMAIL PROTECTED]
> in
alt.algebra.help:
[...]
> I am trying to define a set R(n) for intervals [x,y] and [x',y'] such
that n
> and n' in those intervals are integers indexing columns. The defining
> criteria are outlined below, starting with an explanation of where I am
> coming from.
[...]
> I am pairing values n with n'.
> Let i_1 and i_2 be integers (whether distinct or not) such that 1<=i_1
&
> i_2 <= y.
Did you mean x <= i_1, i_2 <= y? Because if you really
meant the lower bound to be 1, x doesn't figure in your
definitions of pairs (n, n') and therefore shouldn't be
involved in any expression counting such pairs.
> There are (y-x)^2 possible pairs n and n'.
This makes no sense until you've told us what n and n' are.
> This includes pairs
> (n,n') such that n=y-i_1 and n'=y'-i_2, and also (n,n') such that
n=y-i_2
> and n'=y-i_1.
Do you mean that for each i_1 and i_2 in the range specified
above, (y - i_1, y' - i_2) and (y - i_2, y' - i_1) are
possible pairs (n, n'), and that these are the only possible
pairs? If so, the second one is redundant.
> Let C be the set of the possible combinations of (n,n').
> #C=(y-x)^2.
If my interpretation is correct, #C is actually
(y - x + 1)^2, since there are y - x + 1 integers in the
range [x, y] (assuming that x and y are themselves integers
and x <= y).
> Define A' to be a subset of C, such that
> a) #A' = y-x
> b) y>x.
> c) y'-x'=y-x
This makes no sense: what are x' and y'?
I stopped here, because there are already too many
unanswered questions.
[...]
Brian
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