(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to find if 5/27 and 8/9 are in the Cantor set.

2. Relevant equations

[tex]C_2=[0,1/9]\cup[2/9,3/9]\cup...\cup[8/9,1][/tex]

[tex]C_3=[0,1/27]\cup[2/27,3/27]\cup[4/27,5/27]\cup...\cup[26/27,1][/tex]

3. The attempt at a solution

I have: [tex]8/9=(0.22)_3[/tex]

and it is an endpoint in one of the closed sets of C2, so it is in the Cantor set.

I also have: [tex]5/27=(0.012)_3[/tex]

It is an endpoint in C3, but doesn't the 1 in the base 3 expansion mean that it isn't part of the Cantor set?

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# Cantor set fun

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