Logically, must past events be finite in number?

“Yes, after all…
  • An actual infinity can't exist in the world
  • An actual infinity can't be formed by adding

      A collection formed by successive-addition cannot be infinite.1 After all…

      • …any finite quantity plus another finite quantity is always a finite quantity.
      This is relevant because the temporal series of events in the past is a collection formed by successive addition.

      So? Couldn't it simply be that…
      •…Past events have always been infinite in number?
      •…Past events are not successive-additions?

      1. If an infinite number of hours can be “achieved,” then someone can have a infinitieth birthday. Absurdities and internal contradictions abound.
        Ellis, Kirchner, & Stoeger: “The arguments against an infinite past time are strong – it’s simply not constructible in terms of events or instants of time, besides being conceptually indefinite” [G.F.R. Ellis, U. Kirchner, and W.R. Stoeger, “Multiverse and Physical Cosmology,” Monthly Notices of the Royal Astronomical Society, Vol. 347, Is. 3, (2004): 14.]
      2. Graham Oppy: “...if one supposes that time has the structure of the real numbers and if one also supposes that there are continuous processes in time, then one will deny that past events form a series, and one will also deny that the collection of past events fall under a relation of successive addition. … time is modelled by the real numbers in so many of our most successful scientific theories,…” [Arguing about Gods (Cambridge, 2009), 142-143 (Oppy said this also in 2006)]