Hi,
I am not trained in maths but have something I want to express, and
would
be very grateful for advice as to how to write it in a professional, if
not
necessary exclusively mathematicaly formal, manner.
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.
Notation: <= signifies less than or equal to.
>= signifies greater than or equal to.
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. There are (y-x)^2 possible pairs n and n'. 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.
Let C be the set of the possible combinations of (n,n').
#C=(y-x)^2.
Define A' to be a subset of C, such that
a) #A' = y-x
b) y>x.
c) y'-x'=y-x
d) Every n in A' is a unique integer in [x,y] and every n' in A' is a
unique
integer in [x',y'].
e) There are no members of A' such that n>1 and n'=0, or n'>1 and n=0.
For all R(n,n'), (n,n') is a member of A', such that n is greater than n',
and #R(n,n') = n-n'.
Many thanks in advance.
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