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In the text "Classical Real Analysis Second edition(2008)". The famed Cantor Tentary Set is defined in 1.). My initial question is how the Series is constructed/formulated in 1.) ?

$1.)$ $$ C = \Big\{ X \in [0,1]: X = \sum_{n=1}^{\infty}\frac{I_n}{j_n}\Big\} \, for \, I_n=0 \, \, or \, \, 2$$

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    I think $j_n$ in the denominator should be $3^n$, but perhaps the source you quote from is trying for a generalization that can also produce fat Cantor sets, etc. In any case it doesn't look very meaningful to put "for $I_n=0$ or $2$" _outside_ the curly brackets; the $I_n$s must be chosen for _each_ $X$ in the set. – 2017-02-11
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    Ternary, not "tentary." – 2017-02-12
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    Interesting initially I had questions on why the Cantor Set would be represented as a summation rather than countable unions/intersections – 2017-02-21

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