The Infinite Hotel Paradox

The Infinite Hotel Paradox

German mathematician David Hilbert proposed the infinite hotel paradox as a way to illustrate the confounding properties of infinity. It was a way to expound on the theories of Georg Cantor, who proved there were different kinds and sizes of infinities in the late 1800s. Hilbert proposed different mathematical strategies for clearing out rooms in the infinitely booked, infinite hotel to accommodate new guests-even if they arrived in infinite numbers.

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Key Facts In This Video

  • 1

    Taken to its extreme conclusion, the paradox of Achilles and the tortoise suggests that all movement is impossible. (0:48)

  • 2

    German mathematician David Hilbert invented the infinite hotel paradox to illustrate the strange properties of infinity. (3:25)

  • 3

    The twin paradox states that one twin traveling near the speed of light will move through time more slowly than his twin back on Earth. (4:44)

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