(November 18, 2022 at 1:41 pm)Jehanne Wrote:(November 18, 2022 at 1:37 pm)Mister Agenda Wrote: Seems to me like you could have two tallest trees of equal height. No way to prove there's just one without measuring.
The cardinality of the set of primes and that of the natural numbers are identical, even though all the even numbers (except for #2) are not prime.
Infinite rooms, booked solid with all the primes, and a convention of all even numbers shows up looking for rooms. Proprietor David Hilbert says, "No problem!" and sends his bellhop to tell every nth prime to relocate to room 2n so the nth even number can have room 2n-1.
