Recall that
\lim_{x \longrightarrow c} f(x) = L means:

For all\epsilon > 0 there is a \delta > 0 such that for all x
satisfying 0 < |x-c| < \delta we have that |f(x) - L| <
\epsilon .

What if the limit does not equalL ? Think about what the means in
\epsilon,\delta language.

Consider the following phrases:

For all

What if the limit does not equal

Consider the following phrases:

** 1.**

** 2.**

** 3.**

** 4.**

** 5. but **

** 6. such that for all**

** 7. there is some **

** 8. there is some x such that **

Order these statements so that they form a rigorous assertion that

In order to get credit for this problem all answers must be correct.