What if the epsilon-delta definition of a limit reversed the wording for $δ$ and $ϵ$: “for all $δ>0$, there exists an $ϵ>0$ such that, if $0<|x-a|<δ$, then $|f(x)-L|<ϵ$.” Would this definition still capture the concept of limit? Why or why not? If not, give a counter-example.
I want to say "no" this doesn't capture a limit because the definition of a limit must hold true for each and every epsilon. However, I'm not quite sure how to state this or what might be a counter-example.