  In infinitely cyclic cosmology past eras are discussed using set theory and
transfinite numbers. One consistent scenario, already in the literature, is
where there is always a countably infinite number, $\aleph_0$, of universes and
no big bang. I describe here an alternative where the present number of
universes is $\aleph_0$ and in the infinite past there was only a finite number
of universes. In this alternative model it is also possible that there was no
big bang.
