How to resolve this paradox involving Cantor's diagonal argument?

sequences-and-series elementary-set-theory infinity paradoxes

No, it is not in the set. Your set is$$\left\{\frac1{10},\frac{11}{100},\frac{111}{1\,000},\cdots\right\}$$and the number that you get is $\frac19$, which does not belong to it.

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