Seems yea, I'd say infinity is only a limit and can never actually be reached. There's no number that can come before infinity (infinity-1) and it's like the equation y = 1/x. The equation never actually reaches the X axis or y axis
Even if you kept counting all day everyday and removed death, boredom, etc. You will never actually cease counting at a certain point it would just be an infinitesimal series that's not reached