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 initial strategy used by the night manager to accommodate one extra guest in the fully booked Infinite Hotel?

• Ask the guest in room 1 to leave.

• Build an additional room.

• Move each guest from room n to room n+1.

• Charge the new guest extra for a shared room.

How does the night manager accommodate a finite number of new guests, such as a tour bus with 40 people?

• Move each guest from room n to room n+1.

• Build 40 new rooms.

• Move each guest from room n to room n+40.

• Ask 40 guests to share their rooms.

What is the key concept that allows the night manager to accommodate an infinite number of guests from an infinite bus?

• Real number infinity

• Finite infinity

• Countably infinite

• Uncountable infinity

What mathematical concept does the night manager use to accommodate passengers from an infinite number of infinite buses?

• Geometric series

• Arithmetic progression

• Fibonacci sequence

• Prime numbers

How are passengers from the second bus assigned rooms in the Infinite Hotel?

• Using powers of 7

• Using powers of 11

• Using powers of 5

• Using powers of 3

What is the term used by Georg Cantor to describe the level of infinity dealt with in Hilbert's Infinite Hotel?

• Aleph-zero

• Aleph-two

• Aleph-infinity

• Aleph-one

Why are Hilbert's strategies not applicable to higher orders of infinity, such as the real numbers?

• There is no systematic way to include every real number.

• Real numbers include negative numbers.

• Real numbers are finite.

• Real numbers are countably infinite.