\documentclass[10pt]{article}

\usepackage{ngerman,a4,amssymb,amsmath}
\usepackage[latin1]{inputenc}
\usepackage{listings}
\usepackage{enumerate}

\begin{document}

\newcommand{\AND}{\ensuremath{\wedge}}
\newcommand{\OR}{\ensuremath{\vee}}
\newcommand{\SetR}{\ensuremath{\mathbb{R}}}
\newcommand{\SetN}{\ensuremath{\mathbb{N}}}
\newcommand{\SetZ}{\ensuremath{\mathbb{Z}}}
\newcommand{\Inv}[1]{\ensuremath{\frac{1}{#1}}}
\newcommand{\QED}{\ensuremath{\hspace*{\fill}\square}}

Aufgabe 1, Punkt 1

Zum Induktionsschluß:
\begin{eqnarray*}
	T(n) & \le & log(\lfloor log_2(\sqrt{n})\rfloor) \\
	& \le & log(\lfloor log_2(n^{\frac{1}{2}})\rfloor) \\
	& \le & log(\lfloor \frac{1}{2} log_2(n)\rfloor) \\
	& \le & log(\lfloor log_2(n) \rfloor) \\
	& \le & log(n)
\end{eqnarray*}

\end{document}