How An Infinite Hotel Ran Out Of Room

The video explores the concept of Hilbert's Hotel, a thought experiment about infinite rooms and guests. It demonstrates how to accommodate infinite guests using room shifting and spreadsheets. However, it highlights the limitations when dealing with uncountably infinite guests, illustrating that some infinities are larger than others. This concept has profound implications, leading to technological advancements.

What is the initial strategy used by the manager to accommodate a new guest when all rooms are full?

• Evict a current guest

• Build an additional room

• Move each guest to the next room

• Ask the guest to wait until a room is free

How does the manager accommodate a bus with 100 new guests?

• Evict 100 current guests

• Move each guest down 100 rooms

• Ask 100 guests to share rooms

• Build 100 new rooms

What method is used to accommodate an infinite number of guests from an infinite bus?

• Build more rooms

• Ask them to share rooms

• Assign them to odd-numbered rooms

• Assign them to even-numbered rooms

How does the manager handle an infinite number of infinite buses?

• Assign each bus a floor

• Use a spreadsheet to assign rooms

• Ask guests to share rooms

• Build more hotels

What is the key difference between countable and uncountable infinity?

• Countable infinity is finite

• They are the same size

• Countable infinity is larger

• Uncountable infinity is larger

Why can't the Hilbert Hotel accommodate guests with infinitely long names?

• The names are uncountably infinite

• The names are too long

• The guests refuse to share rooms

• The hotel is full

What concept does the Hilbert Hotel illustrate about infinity?

• Infinity is always larger than any number

• Infinity cannot be understood

• Infinity is finite

• Infinity can be manipulated