which lies between them, i.e. <sp

\begin{matrix}
L & \ = { x \mid x \in \mathbb{Q},x \leq 0} \cup \left{ x \mid x \in \mathbb{Q},x > 0,x^{2} < 2 \right} \
U & \ = \mathbb{Q} - L = \left{ x \mid x \in \mathbb{Q},x > 0,x^{2} > 2 \right} \
\end{matrix}$ .

2. A fact between two Dedekind cuts(the density of Q in R): For any pair of real numbers \alpha and \beta, where \alpha > \beta, there can always be found a real, and even in particular a rational, number r which lies between them, i.e. \alpha > r > \beta (and, consequently, an infinite set of such rational numbers).