Constant Functions: ε-δ Proof for Continuity

[Niles]

Homework Statement

Hi all

How can I show that a constant function defined on a closed interval is continuous on that same interval using a ε-δ proof?

I have f(x)=c on the interval. Then I write

f(x)-f(a) = c-c = 0

for some point a in the interval. But what to do from here?

 

[Mark44]

This is a very easy proof. Isn't 0 < epsilon for any positive epsilon?