【無限のふしぎ】満室なのに客が泊まれる「無限ホテル」の謎

Have you ever wondered why a hotel can still accommodate guests when it's fully booked? There are no vacant rooms, yet apparently, there are hotels that can still find new guests. Tonight, we'll slowly unravel just one of these "whys." There's nothing to memorize. And please, don't worry if you fall asleep along the way. About 100 years ago, the German mathematician Hilbert envisioned a hotel to convey the elusive concept of "infinity." An infinite hotel, with rooms stretching on endlessly. In its fully booked corridors, if everyone simply shifts to "the next room," the room at the entrance becomes completely empty. Adding one to infinity still results in infinity. Even halving it still results in infinity. Our usual sense of counting is quietly betrayed. Eventually, the story takes a quiet turn. The hotel that has swallowed up every infinity encounters just one guest it cannot accommodate. Cantor's diagonal argument and the astonishment of the existence of infinitely large and small things. Using familiar metaphors, we gently trace this concept step by step, following corridors, buses, and student registers. ― Table of Contents ― 00:00 Introduction ― Why can they accommodate guests even when the hotel is full? 02:37 Chapter 1 ― Shifting to the next room: The first mystery 09:57 Chapter 2 ― Even with an infinite number of buses, they go to an even-numbered room 18:29 Chapter 3 ― An infinite number of buses, counted diagonally 25:27 Chapter 4 ― An infinite number that cannot be accommodated: The diagonal argument 32:53 Chapter 5 ― Even infinity has big and small 40:53 Conclusion ― At the end of the act of counting, goodnight This video is a meditative explanation of "mysterious trivia" based on scientific, natural, and mathematical knowledge, intended for listening to slowly before bedtime. It includes some interpretive views and poetic expressions. Some of the video and images are generated using AI. ― Wonder Nocturne ― The Mysteries of Sleepless Nights ― #mystery #trivia #mathematics #infinity #infinityhotel #Hilbert #Cantor #diagonalargument #sleepinduction #fallingasleep #backgroundmusic #lullaby #science #sleeplessnights #numbers