Question
Why does nQ denote the set of all irrational numbers?
Background
I'm in my sophomore year of university taking a Theoretical Concepts of Calculus course and one of my professors denoted the set of all irrational numbers by nQ (where Q is the set of all rational numbers). This was strange to me as I couldn't find an example of another source denoting it in this way. Additionally, the only other context where I've seen something similar, is when one denotes a set of multiples, as shown below.
∃n ∈ R ∋ nZ = { nm | m ∈ Z } where R and Z represent the set of all real and rational numbers, respectively.
I've tried playing with the idea of nQ being a shorthand for $\lim\limits_{n \rightarrow ∞} n\mathbf{Q}$, since an irrational number isn't a multiple of any rational number. However, my logic there isn't really fleshed out and doesn't seem particularly sound for a reason unknown to me.
I'm aware that there may be no real reason for denoting the irrationals in this way (since notation is just notation and nothing more), but if there is a reason I would love to hear it!
Note that I'm already aware of some of the more standard ways of denoting the irrationals (e.g. $\mathbf{Q}^c$ and $\mathbf{R} \setminus \mathbf{Q}$).
Thanks in advance!