Notation for an Array What is the proper mathematical notation to deal with an array?
Beginning with the declaration, I am used to the following format as a programmer:
ARRAY:
X[number of elements in array];

FOR i=1 TO 100 BEGIN
X[i]=N[i];
END;

Many thanks.
 A: The word "array" is not a mathematical notion in the way that "vector" or "matrix" are. The mathematical idea that comes closest is family.
Given an arbitrary index set $I$  and a "universe" $X$, a family of elements $x\in X$ is a function $$f:\quad I\to X,\qquad \iota\mapsto x_\iota$$ 
that produces for each $\iota\in I$ a certain element $x_\iota\in X$. Thereby one and the same element $x\in X$ may be produced several times.
This function is not interesting as such, nobody cares about continuity or the like, it only serves to organize the list of $x$'s that we want to study now. When talking about this family we therefore don't mention the actual $f$; instead we denote this family by $(x_\iota)_{\iota\in I}\>$, or by $\ \bigl(x_\iota\, \bigm|\, \iota\in I\>\bigr)\ $ if typographically preferable.
The index set $I$ might have some internal structure by itself. If, e.g., the set $I$ is a cartesian product $I=[m]\times[n]$, where $[m]:=\{1,2,\ldots,m\}$, then a family $(a_\iota)_{\iota\in I}$
is called an $(m\times n)$-matrix.
