Irrational Number

We have $b_n$ a sequence defined by:

$b_n = $ (1 if n is primary, 0 if not)

Let there be a $x \in \R$ such that its decimal representation is $x = 0, b_1 b_2 b_3 ....$

a. Prove that $x \notin \mathbb{Q}$
b. Show that $\frac{1}{91} < x < \frac{1}{90}$

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