@Pablo.Alises
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$$\textbf {Chapter 2: \textit {Number Systems}}$$
$$\textbf {\textit {PROPOSITION 2.1}}$$
$$\textit{Between any two rationals there is another rational.}$$
$$\textbf {\textit {PROPOSITION 2.2}}$$
$$\textit{There is a real number } \alpha \textit{ such that } \alpha ^2 =2.$$
$$\textbf {\textit {PROPOSITION 2.3}}$$
$$\sqrt{2}\textit{ is not rational.}$$
$$\textbf {\textit {PROPOSITION 2.4}}$$
$$\textit{Let a be a rational number, and b an irrational.}$$