# invertibility of $AR(\infty)$?

Here it writes:

"Pure AR models are always invertible (since they contain no MA terms)."

Is this valid also for the limiting case, that is to say, is $$AR(\infty)$$ invertible?
Why or why not?
If not, what are the conditions for $$AR(\infty)$$'s invertibility?

What I did: Every AR(p) model can be written as $$MA(\infty)$$. Hence, the problem reduces to whether this fact is valid in the limiting case; i.e, $$p=\infty$$.