It's okayI'm sure this is a really simple problem, I just wanted to make sure that I'm doing this correctly.
Suppose that \rightarrow R" alt="f \rightarrow R" /> has a limit at . Prove that \rightarrow R" alt="|f| \rightarrow R" /> has a limit at and that .
Proof: Let . Then, such that, if . By the Inverse Triangle Inequality, we have that . Therefore, .