Just to clarify a little bit: For each integer n there is also an infinite amount of rationals (fractions) between n and n+1 and the rationals is also a countab

Just to clarify a little bit: For each integer n there is also an infinite amount of rationals (fractions) between n and n+1 and the rationals is also a countable set like the integers (just as 'infinite', so to speak). Quite counter-intuitive, I think. I usually interpret the first steps in Hilbert's hotel as the first steps in the ordinal hierarchy (https://en.wikipedia.org/wiki/Ordinal_number https://en.wikipedia.org/wiki/Ordinal_number).