A variable for the first 8 integers? I wish to use algebra to (is the term truncate?) the set of positive integers to the first 8 and call it for example 'n'.
In order to define $r_n = 2n$ or similar.
This means:
$$r_0 = 0$$
$$r_1 = 2$$
$$\ldots$$
$$r_7 = 14$$
However there would not be an $r_8$.
edit: Changed "undefined" to "would not be", sorry about this.

You've tagged this abstract-algebra and group-theory but it's not entirely clear what you mean.
However, by these tags, perhaps you are referring to $\left(\Bbb Z_8, +\right)$?
In such a case, you have $r_1+r_7 = 1+_8 7 = 8 \mod 8 = 0$. So there is no $r_8$ per se; however, the re-definition of the symbols $r_0, r_1, \ldots$ is superfluous.
