It is known that there is an infinite number of worlds, but that not every one is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so if every planet in the Universe has a population of zero then the entire population of the Universe must also be zero, and any people you may actually meet from time to time are merely the products of a deranged imagination.

—Douglas Adams

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Unfortunately, Adams confuses/conflates the difference between “infinity” and “uncountable”.

See the following letter (PDF), regarding the traps surrounding inadvertently-undisciplined use of the word “infinity”, in this letter written both in response to a high school student’s query, the student being unsure of the exact meaning about what was being taught, with the letter also being copied to the student’s teacher:

https://people.eecs.berkeley.edu/~wkahan/Infinity.pdf

It is possible to express an integer that is considerably larger than all the atoms that we believe to be in the universe; perhaps something like:

10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^10))))))))))))))

(this is a wild guess on my part, and may fall short, but extending the formula in the obvious fashion should eventually lead to a integer that indeed exceeds the number of atoms).

So, according to Kahan’s very careful use of linguistics, set theory, bijections and other mathematical tools, the number of worlds can be *uncountable*, but defending the proposition that the number of worlds is “infinite” is much harder to defend.

At the end of the day, it is not *known* that there are an infinite number of worlds. This is a fallacy at the start of the quote, and the rest falls down as a result.

— fred.bloggs