Philosophy of Mathspeaking topic

A hotel with infinitely many rooms is completely full, not a single vacancy. Yet you can still make room for a new guest, in fact for infinitely many new guests. How can something that is full still take more?

Hilbert's Hotel

practice with this topic

Set the timer (5-30 min), take 20 seconds of prep if you like, start talking. Jot your thoughts onto the sticky-note board.