The Cantor Set
The Cantor set is defined as follows: Start with the interval [0, 1]. 

The process of getting the Cantor set can be illustrated as follows.

The Cantor set is uncountable and contains no intervals.  It is, perhaps, the earliest example of fractals.  

For a given number x between 0 and 1, x belongs to the Cantor set if and only if there is a ternary representation of x that does not contain the digit 1, that is,

For a rational number x, you can use the following calculator to test it.   

Is it an element of the Cantor set?
Enter a fraction
Numerator / Denominator
or Enter a number in decimal form
 

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