I was wondering about how to define formally in mathematics the use of units of measure.
Initially I was thinking about taking the algebra of rational functions over the indeterminates which are precisely the units ($s, m, g, etc$): $\ \mathbb{R}(m,s,g,\dots).$
This, however, is not much satisfying because I don't really want to add $1s+1m:$ it does not make much sense. The problem is that I don't know a mathematical structure where multiplication is allowed but not addition between the elements with different units (something like monomials).
Maybe you'll find the question stupid or inappropriate, in this case I'll remove it. I'm asking here because I didn't find any answer elsewhere.
