I was recently reading
The Restaurant at the End of the Universe by Douglas Adams, and in it I found the following passage:
Douglas Adams writes:
It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds.
Now let's assume for the sake of argument that the first two sentences are correct. Is the conclusion Adams draws from these two statements correct?
For simplicity, let's say there is only one uninhabited planet. That follows the premises, right? So all but one of the infinite worlds in the universe are inhabited. My question is: Is the number of inhabited worlds finite or infinite?
It seems to me it must be infinite. If it's a finite number, then adding the one uninhabited planet to find the total number of planets would render a finite number, which is impossible given the premise of an infinite number of worlds.
So who's right? Me or Douglas Adams?
Big Bang and Cosmology? Coffee House? Somewhere else?