a)
[tex]1\ \textless \ 2\ \textless \ 4 \Leftrightarrow \sqrt1\ \textless \ \sqrt2\ \textless \ \sqrt4 \Leftrightarrow 1\ \textless \ \sqrt2\ \textless \ 2 \\
\Leftrightarrow 1+2\ \textless \ \sqrt2 + 2\ \textless \ 2+2 \Leftrightarrow 3\ \textless \ 2+\sqrt2\ \textless \ 4 \\ \Leftrightarrow 0\ \textless \ 3\ \textless \ 2+\sqrt2\ \textless \ 4\ \textless \ 5 \Leftrightarrow 0\ \textless \ 2+\sqrt2\ \textless \ 5 \\
\Rightarrow 2+\sqrt2\in i[/tex]
b)
[tex]i=(0,5)\\
(0,5)\bigcap \mathbb{Z}=\{1,2,3,4\}[/tex]
