In this episode we learn about the concept of quantifying infinite sets. The first infinite set that comes to mind is the set of natural numbers introduced before. In consequence, we single out this size of infinity as the one we are most comfortable with. This yields the definition of countability. We also explore a little the intricacies of infinity by looking at a fully booked hotel still capable of hosting additional guests. This famous building is called Hilbert's Hotel and helps us to also understand which of the following sets is quantitatively bigger (ignoring the names of the elements): the natural numbers, the integers or the rationals?