Let $Y, Z$ be random variables and $G$ be a $\sigma$-algebra. Page 69 of Shreve's Stochastic Calculus for Finance II says "because both $Y$ & $Z$ are $G$-measurable, their difference $Y-Z$ is as well". I don't understand how this can be true.

For example, say $Y(\omega) = Z(\omega) = 1$ for all $\omega\in\Omega$ and say that $G=\sigma(Y) = \{\Omega\}$. It's clear that both $Y$ and $Z$ are $G$-measurable, but it doesn't seem to me that $Y-Z$ is. What am I missing?