Cantor\'s Disappearing Table The following procedure shows how to make a table d

Question

Cantor's Disappearing Table The following procedure shows how to make a table disappear by removing only half of the table! (a) Original table has a length of L (b) Remove H of the table centered the midpoint. Each remaining piece has a length that is less than eco Remove t of the table by taking sections of length L from the centers of each of the two remaining pieces. Now, you have removedt +t of the table. Each remaining piece has a length that is less than L (do Remove of the table by uking sections of length from the centers of each of the four remaining pieces. Now, you removed +d +aof the lable. Each remaining piece has a length that is less than will continuing this process cause the table to disappear, even though you have only removed half of the table? why

Explanation / Answer

The Cantor's disappearing table problem is the same as finding the sum of the series 1/4 + 1/8 + 1/16 + ....

This can be written as

S = 1/22 + 1/23 + 1/24 + 1/25 + ......

=>S = 1/22 + 1/2(1/22 + 1/23 + 1/24 +...)

=> S = 1/22 + 1/2 * S

=> S/2 = 1/4

=> S = 1/2

This means the sum is only 1/2. So only half the table will disappear and the entire table won't.

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