How will I know if limits such as $|a_n-L|\Longleftrightarrow|a_n^2-L^2|$ as $a_n \rightarrow L$ are true?
In this case, I know that $|a_n^2-L^2| \Longrightarrow |a_n-L|$ as $a_n \rightarrow L$ is false because $L$ could be negative or that $a_n = L, -L, L, -L, ...$, but how do I determine if $|a_n-L| \Longrightarrow |a_n^2-L^2|$ is true?
Thank you!