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\begin{document}

\begin{center}
\textbf{Proprietatile modulului}
\end{center}

\begin{enumerate}
\item $|a|\geq a$.
\item $|a|\geq -a$.
\item $|a|=|-a|$.
\item $|a|\geq 0$ si\\
      $|a|=0$ daca si numai daca $a=0$.
\item $|a|=a$ daca si numai daca $a\geq 0$.
\item $|a|=-a$ daca si numai daca $a\leq 0$.
\item $|a|=\sqrt{a^2}$.
\item $|a+b|\leq |a|+|b|$ si\\
      $|a+b|=|a|+|b|$ daca si numai daca $ab\geq 0$.
\item $|a\cdot b|=|a|\cdot |b|$.
\item $\ds \left|\frac{a}{b}\right|=\frac{|a|}{|b|}$.
\item $|a|=b,\ b\geq 0\ \Lr\ a=\pm b\ \Lr\
      \left[
      \begin{array}{l}
        a=b,\\
        a=-b.
      \end{array}
      \right.$
\item $|a|<b,\ b>0\ \Lr\ -b<a<b\ \Lr\
      \left[
      \begin{array}{l}
        a<b,\\
        a>-b.
      \end{array}
      \right.$
\item $|a|>b,\ b>0\ \Lr\
      \left[
      \begin{array}{l}
        a>b,\\
        a<-b.
      \end{array}
      \right.$
\item $|a|=|b|\ \Lr\ (a-b)(a+b)=0\ \Lr\ a=\pm b$.
\item $|a|>|b|\ \Lr\ (a-b)(a+b)>0\ \Lr\ a\in (-\infty;-|b|)\cup
      (|b|;+\infty)\ \Lr\ -|a|<b<|a|$.
\item $|a|^2=a^2$.
\end{enumerate}

\footnotetext[0]{\quad Copyright$\copyright$1999 ONG TCV
    Scoala Virtuala a Tanarului Matematician \quad http://math.ournet.md}


\end{document}
