Josephood7

Recall that

means:
For all ϵ>0ϵ>0 there is a δ>0δ>0 such that for all xx satisfying 0<|x−c|<δ0<|x−c|<δ we have that |f(x)−L|<ϵ|f(x)−L|<ϵ.
What if the limit does not equal LL? Think about what the means in ϵ,δϵ,δ language.
Consider the following phrases:

1. ϵ>0ϵ>0
2. δ>0δ>0
3. 0<|x−c|<δ0<|x−c|<δ
4. |f(x)−L|>ϵ|f(x)−L|>ϵ
5. but
6. such that for all
7. there is some
8. there is some xx 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: