# Math Help - Proof with inequalities

1. ## Proof with inequalities

Sorry if this is in the wrong place, couldn't think of where to put this; the module's called The Foundations of Calculus, but yeah...

Suppose that $\epsilon>0$. Prove that if $x,l,y\in\mathbb{R}$ and $|x-l|,|y-l|<\frac{\epsilon}{2}$ then $|x-y|<\epsilon$.

I've tried a few stuff with the triangle inequalities and what not and they've lead no where

2. $|x-y|=|x-l-y+l|\leq |x-l|+|l-y|=|x-l|+|y-l|<2\frac{\epsilon}{2}=\epsilon$