cyrano@lemmy.dbzer0.com to Science Memes@mander.xyzEnglish · 8 days agoInfinite Hotel Paradoxlemmy.worldexternal-linkmessage-square36fedilinkarrow-up1461arrow-down110file-textcross-posted to: [email protected]
arrow-up1451arrow-down1external-linkInfinite Hotel Paradoxlemmy.worldcyrano@lemmy.dbzer0.com to Science Memes@mander.xyzEnglish · 8 days agomessage-square36fedilinkfile-textcross-posted to: [email protected]
cross-posted from: https://lemmy.world/post/25703033 https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel
minus-squareGladaed@feddit.orglinkfedilinkEnglisharrow-up8·7 days agoIf you have n rooms and n guests there are no empty rooms. Let n go to infinity and there should still be no empty rooms. The trick of the Hilbert hotel is that if you add a guest to a hotel with countably infinite guests the number of guests does not change.
If you have n rooms and n guests there are no empty rooms. Let n go to infinity and there should still be no empty rooms.
The trick of the Hilbert hotel is that if you add a guest to a hotel with countably infinite guests the number of guests does not change.