If you take an ordered field of numbers with the operations of addition and multiplication, endowed with the completeness axiom, represent in as an infinite series of points constituting a line, then put three such lines orthogonal to each other, it does not seem obvious to me that this is the exact three-dimensional space satisfying Euclid's five axioms. Is there a formal proof of the equivalence of these two spaces, and if there is where can I find it ?(adsbygoogle = window.adsbygoogle || []).push({});

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# R^3 and E^3, are they the same?

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