A transition metal can be defined as an element that possesses an incomplete sub-level in one or more of its oxidization states. In the textbook I'm reading, it claims that zinc is not a transition metal because it has a full $d$-sub-level in all its oxidization states.
A quick google reveals that zinc has oxidization states $-2, 0, +1$, which means that zinc(with oxidization number $+1$) has an incomplete d-sub-level and is a transition metal.
What's going on here? Is my textbook incorrect?
Zinc in the +1 oxidation state is $\text{[Ar]}3d^{10}4s^1$, and even in its highest, most common known oxidation state +2 (which the quoted values above seem to have forgotten) it's still $\text{[Ar]}3d^{10}$. No known zinc species in what we normally consider the realm of chemistry breaks that complete $3d^{10}$ subshell, and we would need a major revamp of our calculations and models if any ever does. Moreover, the thermophysical properties of zinc also betray a loss of transition-metal character. Zinc is just not a transition element.
As a followup to my question, I want to state $\ce{Zn}$ is not a transition metal also because of the Aufbau Principle. According to the principle, electrons are removed from the subshell with the highest quantum number first. So in a case such as $\ce{Zn^2+}$, electrons are moved from the $4s$ subshells instead of the $d$-subshells. The $d$-subshell remains full.
