When is it more appropriate to describe steps using English rather than mathematics?

Question

For example, are there set cases when one would write "$x$ is a positive integer" instead of writing "$x \in \mathbb{Z}^{+}$", or vice versa?

Answer 1

I will only use notation if it's relevant in some way to the calculation I'm doing or simplifies the presentation of the ideas being discussed. If I ensure that the notation is useful in some meaningful way then I find I can justify using it, otherwise it may simply be clutter.