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Recognitions:
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$$z_n = \frac{\left[ x *10^{n-1} \right] + \left[ y * 10^{n-1} \right]}{10^{n-1}}$$
$$\lim_{n \rightarrow \infty} z_n = z$$
You can 'evaluate' edition this way, it doesn't make much sense to do so but it is a way of show addition can be described as an iterative procedure for $x, y, z \in \mathbb{R}$ in terms of adding numbers of integers, which themselves can be expressed as iterative procedures.