This is correct, of course, but...
Originally Posted by Jens
...this isn't. AFAIK.
The big bang seems to indicate it is finite
The evidence for the so-called Big Bang model indicates that the current state of the observable universe had a begining within a finite span of time, but it doesn't really conclusively and certainly tell us if there was or was not something before that nor yet does it proscribe a spatially finite universe.
While it might be a very long shot to assume information has passed through the Big Bang event or will survive indefinitely into the future -- so no infinite time, really -- it isn't overruled that we exist in a Tegmark level 1 multiverse -- which will give us infinite monkeys.
It's another thing of course that most of those "monkeys" probably will never be able to send us any of their "versions of Shakespeare's works" since they won't be able to causally interact with us.
The dog, the dog, he's at it again!