Unfortunately I am stuck on one step of a proof for an algebraic limit theorem, specifically:
Why is it exactly that $\left|b_n - b \right| < \frac{\left|b \right|}{2} \Rightarrow \left| b_n \right| > \frac{\left|b \right|}{2}$ ?
If this doesn't make sense without more context, please let me know. Otherwise, thank you for your help!