Before starting the proof, you must be familiar with the triangle inequality, which states that:
Now lets say:
For every number [ε/2 > 0], there is a number [δ1 > 0] and [δ2 > 0] such that:
Lets say [δ = min{δ1,δ2}]:
If we use the triangle inequality, we get:
So it means we concluded that:
Which basically means:
