abstract.tex

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\begin{abstract}
    %\blindtext[1]
    We present a simple algorithm for the \texttt{3SUM} problem for a list $L$ of $n$ real numbers. For this, we generate real numbers with the help of a set $\mathbb{I}_{a}$ of so called 'Atomic irrational numbers'. We can show that our algorithm, which use the binary representation of integers, takes time complexity $\mathcal{O}\left(nb + U^{1.58}\right)$ for an universe of $U := 2^{b}$ distinguishable rational numbers and with our so generated real numbers it takes a time complexity of $\mathcal{O}\left(nb|\mathbb{I}_{a}| + U^{1.58}_{\mathbb{I}_{a}}\right)$ on an universe of $U_{\mathbb{I}_{a}} := 2^{b |\mathbb{I}_{a}|}$ distinguishable real numbers.
\end{abstract}
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