The addition rule has an absolute value sign. That is

$$ s_{tot}= |s_1 + s_2|,|s_1 + s_2 - 1|, \ldots, |s_1 - s_2| $$

And so the smallest value you can have is $1/2 - 1/2 = 0$.

The addition rule has an absolute value sign. That is

$$ s_{tot}= |s_1 + s_2|,|s_1 + s_2 - 1|, \ldots, |s_1 - s_2| $$

And so the smallest value you can have is $1/2 - 1/2 = 0$. $s_{tot} $ is the thing we use to label the irreducible representations, not $m$.