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What are some interesting applications of the Archimedean Property?

MathOverflow Asked by fisura filozofica on November 3, 2021

So a wile back I managed to prove the The Remainder Theorem starting from the Archimidean property and since then I’ve thought what could be other results which can be proved using it. But I haven’t found any other applications for the Archimidean property, except some very small, almost trivial, results in Analysis. So are there any important results that use it?

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