Explain why this is no good as a definition of continuity

[gregy6196]

Explain why this is no good as a definition of continuity at a point a (either by giving an example of a continuous function that does not satisfy the definition or a discontinuous one that does):
Given ε > 0 there exists a $\delta$ > 0 such that |x – a| < $\epsilon$ $\Rightarrow$ |f(x) – f(a)| < $\delta$

 

[mathman]

There will always exist δ. For example f(x)=0 for x< 0 and f(x) = 1 otherwise. Then your definition will have continuity at 0 using δ > 1.