Let's say I have two nonnegative rational quantities – e.g., time and potatoes – that I want to represent by (potentially infinite) sets of elements $T$ and $P$.
What would be a correct mathematical (formal) definition for that?
Intuitively, I would write $T \overset{\text{def}}{=} P \overset{\text{def}}{=} \mathbb{Q}_{\ge0}$; with $T$ measured in seconds, and $P$ measured in potatoes. Assuming it is a correct way to present it, it is not a formal definition, however$\dots$
Thanks in advance for your answers.
NS