# Eternity universe

## Main Question or Discussion Point

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
Homework Helper
2019 Award
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.