For
let
be the number whose
-th digit after the decimal point is the
-th digit after the decimal point of
. Show that if
is rational then so is
.
%V0
For $x \in (0, 1)$ let $y \in (0, 1)$ be the number whose $n$-th digit after the decimal point is the $2^{n}$-th digit after the decimal point of $x$. Show that if $x$ is rational then so is $y$.
Školjka