In infinity, is repetition inevitable?

      Of course, the concepts of infinite space and time are rooted in the observations and calculations of cosmologists, and I will leave those discussions to them. My question is more of what a possible infinite extension of space and time, as in an ever-inflationary/expanding universe, would imply about repetition.

     When we say "infinite," we of course know what we mean. But to really think that space and time is never, never, never ending .... leads to a conundrum in the back of my mind when I read all these discussions of cosmology. 

     Does infinity imply that structures we see, ideas we see - planets, moons, suns, life, people - have to, at least in some way, repeat themselves? If there truly is no end to the extent of the universe, if time really has no end (and I'm not at all saying this is the case, of course), but if it were, would these entities have to arise again? Not, of course, simultaneously, but at some time in that infinite, never-ending timescale?

     Millions, billions, trillions of years in the never-ending future or past, would another Earth have to exist? Another moon? Another Earth on which life, just like ours, arises? Infinite - there is no limit, there is no end. 

     Fundamentally, I believe the answer is no. We are each unique. We - you and I - cannot be repeated. No other human that looks exactly like me and thinks exactly like me could ever arise, even if time is never-ending. No, the same Earth would not arise again. But, mathematically, it seems to me, never-ending implies all these things have to occur again. 

     It's scary when imagination collides - or works together with! - thoughts of infinity.