Example
Define that
Solution
Assume ε > 0. We find a number δ > 0 such that, if 0 < | x - a | < δ, then | (mx + n) - (ma + n) | < ε.
What we need to do first is set up a connection between | (mx + n) = (ma + n) | & | x - a |. The connection is easy:
| (mx + n) - (ma + n) | = | m | | x - a |.
To make | (mx + n) - (ma + n) | < ε, we require only make | x - a | < ε/ | m |
This recommends that we select 
Therefore, if 0 < | x - a | < δ, then | (mx + n) - (ma + n) | < ε.
Thus
