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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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Puzzle Thoughts Comment 6 of 6 |
f(x)=0 if x=1/2
=4x if there exists a positive integer n such that x=2^(-n-1)
= x if x is between 0 and 1 and if for all integer n, x does not equal 2^(-n)

  Posted by K Sengupta on 2023-07-05 23:50:30
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