The Infinite Hotel

The Infinite Hotel, also known as Hilbert's Hotel, is a thought experiment in mathematics that illustrates the concept of infinity. Imagine a hotel with infinitely many rooms, all occupied. If a new guest arrives, the hotel can still accommodate them by moving each current guest from room n to room n+1, freeing up room 1. This scenario shows that infinity is counterintuitive—an infinite set can still make room for more, despite being full. It highlights fascinating properties of infinity and challenges our understanding of size and space in mathematics.