I am struggling with the concept of Units and the Reduced set of residues. I know that a unit is defined to be an element $(a)$ s.t there exists and inverse element $\hat{a}$. where $\hat{a} * a = 1$. and that an extension of this definition is that $\gcd(a,m) = 1$. But I also have the definition of the reduced set of residues (mod(m)) as being all the elements where $\gcd(a,m) = 1$.
So does this mean that the set of units $U_m$ is the same as the $RsR_m$ ?