What do you mean by cosmos?
Perhaps it would help if I outlined the way in which I use a few terms. It might be good if others, who use these terms differently posted their versions as well.
1. Universe: following John Gribbin, this is what started with the Big Bang. It is what we observe around us, and what I believe is finite.
2. universe: this could be any member of a multiverse, or any theoretical universe that might be under discussion.
3. cosmos: anything, including our Universe or a multiverse which may, or may not extend beyond that which we can observe, detect or definitely prove to exist. Personally, I believe that it is the cosmos, within this definition, that is infinite.
4. infinite: that which is all-embracing, boundless and eternal. Nothing that exists can be separate from infinity, nor can anything that is at any point finite become infinite. Our Universe may be unbounded; it may continue to expand for ever, but it will never become infinite.
5. eternal: because we are constrained to think in 4-D terms, we find it necessary to impute to infinity a temporal facet. This distinction exists only in our limited perception.
how many integers are there? Infinitely many.
I wondered who would be the one to raise this argument.
Up until the early nineteenth century, mathematical existence was rather similar to physical existence. Both were considered to exist in the real world. The discovery of non-Euclidean geometries changed that view. Mathematical ‘existence’ came to mean only logical self-consistency and this did not require physical existence to complete it. If mathematicians could write down sets of non-contradictory axioms, and formulate rules for deducing true statements from them, then those statements were held to ‘exist’. If there can be such a profound difference between physical and mathematical “existence”, or “truth” then it seems reasonable to identify a similar difference between physical and mathematical infinities. The infinite series is entirely a mathematical entity.
If it slows in the Earth's atmosphere then it's <c, so it experiences passage of time,
Let us not forget that even when light is travelling at "c" we, in our F of R perceive a passage through time. Can we be sure that the apparent reduction of the speed of light in the Earth's atmosphere is not also a feature of our limited perception? Why should there be any change, of any sort, in the F of R of the photon?
