Name: TED-Ed】《無限酒店悖論》--傑夫-德科夫斯基。 (【TED-Ed】The Infinite Hotel Paradox - Jeff Dekofsky)
Uploaded: 2021-01-14T04:58:26.000Z
Duration: 6 min

向世人展示要了解「無限」的概念

to wrap our minds around the concept of infinity.

Imagine a hotel with an infinite number of rooms

試想一間擁有無限多間客房的旅館

和一名非常努力工作的夜班經理。

One night, the Infinite Hotel is completely full,

有一晚，這間旅館的房間均已客滿

totally booked up with an infinite number of guests.

the night manager decides to make room for him.

這名夜班經理決定為他騰出一間空房。

很簡單，經理先將原先入住1號房的客人

將原先入住2號房的客人安置至3號房，

Since there are an infinite number of rooms,

there is a new room for each existing guest.

每一位既有的房客都能夠搬到新的房間，

This leaves room 1 open for the new customer.

於是新的客人便得以入住1號房。

只要新房客的數目是有限可數的。

就能將前40間房都空出來給新客人。

with a countedly infinite number of passengers

Now, the infinite bus of infinite passengers

這輛載滿無限多名乘客的無限大遊覽車

Each current guest moves from room number "n"

每一位既有的房客都從原先入住的n號房

filling up only the infinite even-numbered rooms.

便只有無限間數的雙號房會有人住

all of the infinitely many odd-numbered rooms,

而無限大的遊覽車上所乘載的無限多名乘客

Everyone's happy and the hotel's business

banking an infinite number of dollars a night.

每一晚都賺進無限可數的利潤。

Word spreads about this incredible hotel.

這間不可思議的旅館名氣越來越響亮

each with a countedly infinite number of passengers.

每輛巴士上都載滿了無限可數的乘客。

Euclid proved that there is an infinite quantity

So, to accomplish this seemingly impossible task

於是為了達成這項看似不可能的任務

the night manager assigns every current guest

raised to the power of their current room number.

再依該房客原本入住的房間號碼次方的房間號碼。

So, the current occupant of room number 7

接著，夜班經理將無限多輛巴士中

再依每一名乘客在巴士上的座號次方

raised to the power of their seat number on the bus.

So, the person in seat number 7 on the first bus

如此一來，第一輛巴士上坐在7號座位的客人

第一輛巴士上的客人皆經此安排。

are assigned powers of the next prime, 5.

所各自入住的房號則是下一個質數5的座號次方