TED-ED: The Infinite Hotel Paradox - Jeff Dekofsky

The video explores Hilbert's Infinite Hotel, a thought experiment by David Hilbert, illustrating the complexities of infinity. It describes how a hotel with infinite rooms can accommodate new guests, even when full, by shifting guests to new rooms. The video further explains handling infinite buses of guests using prime numbers for room assignments, highlighting the concept of countable infinity, or aleph-zero. It contrasts this with the challenges of a hotel dealing with real numbers, emphasizing the difficulty of grasping infinity.

What is the significance of prime numbers in the room assignment process?

How does the night manager assign rooms to the guests from the infinite buses?

What challenges arise when considering higher orders of infinity compared to countable infinity?