For 1b use what you know from 1a.

.

Show that is a bijection.

For #2 consider the function on .

For #3 define for ease of notation.

Define a function 0,1] \mapsto (0,1)\;,\;\Phi (x) = \left\{ {\begin{array}{rl}

{\frac{1}

{{n + 1}},} & {x = \frac{1}

{n} \in F} \\

x, & {\text{else}} \\

\end{array} } \right." alt="\Phi 0,1] \mapsto (0,1)\;,\;\Phi (x) = \left\{ {\begin{array}{rl}

{\frac{1}

{{n + 1}},} & {x = \frac{1}

{n} \in F} \\

x, & {\text{else}} \\

\end{array} } \right." />