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Open = Closed (Posted on 2005-02-07) Difficulty: 3 of 5
Find a one-to-one correspondence between (0,1) and [0,1].

For those who don't understand the above sentence, (0,1) is the set of all numbers in-between 0 and 1, while [0,1] is the set of all numbers between 0 and 1, including 0 and 1 themselves. You must find a function that matches every number in the first set with a single number in the second set so that each number in each set is used exactly once.

See The Solution Submitted by Tristan    
Rating: 4.1667 (6 votes)

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Solution solution (spoiler) | Comment 2 of 5 |

Map [0,1] to itself, except for 0, 1 and positive integral powers of 1/2 and 1/3.

Map 0 to 1/2 and 1 to 1/3.

Map all (1/2)^n to (1/2)^(n+1) for all positive integral n.

Map all (1/3)^n to (1/3)^(n+1) for all positive integral n.


  Posted by Charlie on 2005-02-07 18:55:59
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