OK, I worked it out. When we are talking about spacetime, (as we imagine it) as a torus. This is the cyclic part. For whatever 'reason', the torus goes through phases of expansion and contraction, with nexuses (I would have preferred nexi) which I see as BHs and BBs. The Universe so imagined is "infinite" in so far as it is timeless and there is nothing "outside" the torus. That is an "infinite" which is self-contained and goes back on itself. Information (at least on a personal level) is not transferred through nexuses.
Then there is the "infinity" I cannot abide. such as 1/0. This is a mathematical abstraction and, imho, has no relevance in the real world. Similarly the problems of infinity 'outside' the Universe, which
quod effuderis is nonsense, (from the definition. These are largely based on anthropocentric inability to conceive of examples such as the first case (above) and they think of a flat "going on forever" because they cannot comprehend a torus of spacetime. Hence you get what comes after the last infinite number, and what is there beyond the last bit of space.
What do you think? Have I solved the question of "two kinds" of infinit(e)(y)?
Cat