My textbook says that $\delta S_{rev}= \frac{q_{rev}}{T}$. It also says that $\delta S_{surr}= \frac{-q_{rev}}{T}$. Logically, this should mean that the change in entropy in both the surroundings and the system are equal in magnitude but opposite in sign.
This is NOT true, though, as it would go against the Third Law of Thermodynamics. Also, my book proves the Law by comparing the equation for $\delta S_{surr}$ to the Entropy of the system found when subtracting the products' entropies from the reactants'.
Where am I going wrong? Why can't we compare the two $\delta S$ equations and disprove the Third Law?
Note: The first equation is $q_{rev}$ due to something to do with a reversible, isothermal reaction that I don't really understand, which might be the source of my confusion...