Learning /
A hotel with no last room
The thought experiment that made infinity feel a little less abstract.
Imagine a hotel with rooms numbered 1, 2, 3, and onward forever. Every room is occupied. An extra guest arrives. Is the hotel full?
Move the guest in room 1 into room 2, the guest in room 2 into room 3, and so on. Everyone keeps a room, and room 1 is now free. There is no last guest to displace.
For infinitely many new guests, move each existing guest from room n to room 2n. The even-numbered rooms hold the original guests; the odd-numbered rooms are available for newcomers.
This is the part worth sitting with: a collection can have the same infinite size as one of its proper subsets. It's a mathematical thought experiment, but a wonderfully concrete way to start a conversation.