5. As you work through your proof, think about what kinds of objects your symbols represent. For example, suppose $A$ is a set and $f(x)$ is a real-valued function. Then the expression $A+f$ might make no sense if we have not defined what it means to “add” a set to a function, so we can stop at that point and adjust accordingly. On the other hand we might understand $2f$ to be the function whose rule is described by $(2f)(x)=2f(x)\text{.}$ “Think about your objects” means to always verify that your objects and operations are compatible.