Archimedean property
= Archimedean property
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{title2=$\forall x\in\mathbb R\ \exists n\in\mathbb N:\ n>x$}
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The Archimedean property says that the <natural numbers> are unbounded in the <real numbers>. In particular, for every positive <real number> $a$ there is a positive <integer> $n$ with $1/n<a$. Otherwise a purported upper bound for all <natural numbers> contradicts the <least-upper-bound property> by translating that bound by one.