Bellhop at the Hilbert Hotel

In 1924,  mathematician David Hilbert imagined a hotel with infinite rooms.

In 'Bellhop at the Hilbert Hotel' you take on the role of an intrepid employee at an infinite hotel escorting guests to their rooms. To do this, you must keep an alphabetized mental list of all the couples you meet. That's a bit of a mental load but save some brain space for observing the visual details around you because there will be a quiz!