You don’t always want to encounter infinity in a strange hotel:
This comic started to take shape when I stumbled across a particular axiom of number theory in an article on “the Moore method”; namely:
AXIOM 1 If x and y are any two different points, there is a point between them…
It sounds simple enough, but in fact it is a deep dark rabbit hole through the thin ice of our day-to-day integer-based concept of numbers… Will our hero ever find the room “next to” his? What’s wrong with this conception of numerical sequence here in the Infinite Hotel?
(And thanks to David Hilbert for the conceptual setting… or should I say George Gamow?!)
ASIDE: After drawing this comic, I did in fact try to get some sleep in my altogether finite hotel room in downtown Manhattan. The radiator was stuck on “hyper” and so the room became oppressively hot…
Nonetheless, I crawled “between” the two thin sheets and somehow managed to drift off to sleep eventually, dreaming sweet dreams of infinity and sequences of points along numberlines…
In the morning I awoke and discovered to my surprise that (and I swear I am not making this up) there was actually a THIRD sheet between ME and the FITTED SHEET on the bed…
For that brief confused moment “between” sleeping and waking, I truly believed (with a touch of horror) that the Infinite Hotel was playing tricks on me…
www.MarekBennett.com 
How does this hotel deal with irrational numbers? The complex numbers? Oh goodness, what am I talking about and where am I going with this…
Yes, it turns out Irrational Room Service is a whole other menu system, and much trickier to dial up… And just TRY getting ANY kind of service in an Imaginary room!