True/false question: limit of absolute function I have this true/false question that I think is true because I can not really find a counterexample but I find it hard to really prove it. I tried with the regular epsilon/delta definition of a limit but I can't find a closing proof. Anyone that

If $\lim_{x \rightarrow a}  | f(x) | = | A |$ then $ \lim_{x \rightarrow a}f(x) = A  $


Let $f$ be constant $1$ and $A:=-1$.
