The Infinity of Days in the Eternity Universe

[thinkandmull]

My question perhaps is assuming there is a multiverse, but its more of a mathematical question. If the universe or universes have existed forever, will the number of days that have been be a countable infinity or uncountable?
Thanks

 

[bapowell]

The number of universes is an integer, as is the number of days. So I'd guess countable.

 

[jbriggs444]

My question perhaps is assuming there is a multiverse, but its more of a mathematical question. If the universe or universes have existed forever, will the number of days that have been be a countable infinity or uncountable?

This is not a physical question. It is purely speculative and purely mathematical.

Suppose that we treat "today in this universe" as the beginning of a binary sequence (e.g. of coin flips).
Each day a coin is flipped. In one multiverse the result is 0 (heads) and in another the result is 1 (tails).
If this process is continued indefinitely, you ask, in effect, "how many coin flips are there altogether".

The answer is, counter-intuitively, that even though there are uncountably many multiverses (uncountably many infinite binary sequences), there are only countably many coin flips in those sequences (*). Every coin flip that will ever be or could ever be only occurs after a finite time. At any particular finite time, there are only finitely many prior sequences of flips. So every flip there ever is or will ever be can be described by a finite integer.

(*) One resolution to the apparent paradox is to realize that there is no one to one correspondence between days and sequences. Each coin flip at the end of a finite sequence is "shared" by uncountably many continuations of that sequence.