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From wikipedia, the cantor function is defined as follows:

Express x in base 3. If x contains a 1, replace every digit after the first 1 by 0. Replace all 2s with 1s. Interpret the result as a binary number. The result is c(x). 

However if I use $x=0.111, y=0.102$ in base 3. Then $x>y$. But the first two steps would give $\phi(x)=0.100$ and $\phi(y)=0.101$ under base 2. Then $\phi(x)<\phi(y)$. How to explain this? I have not examined wikipedia's definition is really compatible with the other definition provided.

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    Are you supposed to replace all digits after the first $1$ by $0$ before you replace all $2$s with $1$s? I think you should get $\phi(x) = \phi(y) = 0.100$.2012-09-11
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    Every digit? ....my god. Thanks.2012-09-11

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