39 lines
803 B
TeX
39 lines
803 B
TeX
\documentclass{article}
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\usepackage{amsfonts, amsthm}
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\usepackage{hyperref}
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\newtheorem{theorem}{Theorem}
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\newtheorem{custominner}{Theorem}
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\newenvironment{custom}[1]{%
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\renewcommand\thecustominner{#1}%
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\custominner
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}{\endcustominner}
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\begin{document}
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\begin{custom}{1.29}
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For every real $x$ there exists a positive integer $n$ such that $n > x$.
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\end{custom}
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\begin{proof}
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\href{Chapter_I_3_10.lean}{Apostol.Chapter\_I\_3\_10.Real.exists\_pnat\_geq\_self}
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\end{proof}
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\begin{custom}{1.30}[Archimedean Property of the Reals]
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If $x > 0$ and if $y$ is an arbitrary real number, there exists a positive integer $n$ such that $nx > y$.
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\end{custom}
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\begin{proof}
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\href{Chapter_I_3_10.lean}{Apostol.Chapter\_I\_3\_10.Real.pos\_imp\_exists\_pnat\_mul\_self\_geq}
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\end{proof}
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\end{document}
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