Is it correct to write $(a,b,c) < d$?

Question

I want to say that the scalars $a$, $b$, and $c$ are all smaller than $d$. Is it mathematically correct if I write it like $$(a,b,c) < d?$$

Answer 1

The standard way to write it is $a,b,c<d$. Since $(a,b,c)$ is a three-dimensional vector, and there is no canonical way to order vectors—let alone compare vectors with scalars—the notation $(a,b,c)<d$ makes no sense. However, if the elements of a finite set $A$ are orderable, it makes sense to write $\max A<d$ or $\max\{a,b,c\}<d$, where $A=\{a,b,c\}$.

Answer 2

As it is just notation, there is no correct or incorrect. It is not common, I would say. You could use $\max(a,b,c) < d$ to avoid ambiguities.