Hello,

I am asked to show that the following two definitions of the limit $\displaystyle L$ of a sequence $\displaystyle s_{n}$ are equivalent:

a) $\displaystyle \forall \epsilon>0 \exists N\in \mathbb{Z} \forall n \geq N: abs(s_{n}-L) < \epsilon$

b) $\displaystyle \forall m \in \mathbb{Z}_{+} \exists N\in \mathbb{R} \forall n \geq N: abs(s_{n}-L) < \frac{1}{m}$

I do see it intuitively, but how do I show it quantitatively?

Thanks.