# Math Help - Lipschitz Continuous

1. ## Lipschitz Continuous

I know this proof should be short and sweet, but maybe there is something that I'm missing. I need to prove that every Lipschitz mapping is uniformly continuous. The map f: A c R --->R. I know the definition of Lipschitz is C=>0 ||f(x)-f(y)||<= C||x-y||

I assumed that the function is Lipschitz, but I don't know what to do next. Should I let E>0 exist? I am not sure if I can create an epsilon..

Thanks!

2. Originally Posted by EricaMae
to prove that every Lipschitz mapping is uniformly continuous. The map f: A c R --->R. I know the definition of Lipschitz is C=>0 ||f(x)-f(y)||<= C||x-y||
Is this something new? I have seen it three times now.
The historical Lipschitz condition requires $C > 0$.
If $\varepsilon > 0$ the let $\delta = \frac{\varepsilon }{C}$.
Then it is simple.