Proportionality In two Values Equal to $0$

Question

If two values $m$ and $n$ are in direct variation, then

$m \propto n$

If the constant of proportionality is $q$ between them, then

$m = qn$

If $m$ and $n$ both are equal to zero or $m = 0$ and $n = 0$, then will they be called directly proportional to each other?

Answer 1

Yes, but trivially so, in that the constant of proportionality can be any non-zero real number. That simply means than the direct proportionality of $m = n = 0$ is independent of the constant of proportionality $q$.

Typically, the sole restriction for two variables $m, n$ to be directly proportional is that the constant of proportionality, $q$ in your case, is non-zero.

See direct proportionality for more information.