Originally Posted by

**FishStyx** Prove the following:

If $\displaystyle \{b_n\}_{n=1}^{\infty}$ converges to $\displaystyle B \neq 0$ and $\displaystyle b_n \neq 0$ for all $\displaystyle n$, then there is an $\displaystyle M > 0$ such that $\displaystyle |b_n| \geq M$ for all $\displaystyle n$.

Now, this sounds very similar to a Lemma that was proven in class.

If $\displaystyle \{b_n\}_{n=1}^{\infty}$ converges to $\displaystyle B$ and $\displaystyle B \neq 0$, then there is a positive real number $\displaystyle M$ and a positive integer $\displaystyle N$ such that, if $\displaystyle n \geq N$, then $\displaystyle |b_n| \geq M$.