Find an f that satisfies these statements - Deltas and Epsilons

[Numnum]

Homework Statement

Find an f that satisfies this statement:
$$\lim_{x\rightarrow a} f(x)≠L$$

$$∀ε>0 ∃δ>0∃ x:0<|x-a|<δ AND |f(x)-L|<ε$$

Homework Equations

The Attempt at a Solution

I'd just like a small hint on how I would go about finding a function. How can there be a delta for every epsilon and the rest of the statement is fulfilled, but there is no limit? The notation's just a tad confusing.

 

[Dick]

Homework Statement

Find an f that satisfies this statement:
$$\lim_{x\rightarrow a} f(x)≠L$$

$$∀ε>0 ∃δ>0∃ x:0<|x-a|<δ AND |f(x)-L|<ε$$

Homework Equations

The Attempt at a Solution

I'd just like a small hint on how I would go about finding a function. How can there be a delta for every epsilon and the rest of the statement is fulfilled, but there is no limit? The notation's just a tad confusing.

You aren't quantifying this right. There just has to be one epsilon without any corresponding delta. lim x->0 x isn't equal to 1. Prove it.