$\displaystyle lim(a_n)=a, lim(b_n)=b$

Prove:

if $\displaystyle a<b$, then there is an index $\displaystyle n_0$ so that for every $\displaystyle n>=n_0$ : $\displaystyle a_n$ $\displaystyle < b_n$

This one should be really easy, I just have no idea how to look at it... Any tips for calculus will be absolutely great!