Recall that 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 equal $L$? Think about what the means in $\epsilon,\delta$ language.
Consider the following phrases:

1. $\epsilon > 0$
2. $\delta > 0$
3. $0 < |x-c| < \delta$
4. $|f(x) - L | > \epsilon$
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 and enter their reference numbers in the appropriate sequence in these boxes:

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