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Talk:Euclidean space

From Encyclopedia of Mathematics
Revision as of 21:34, 3 March 2018 by Boris Tsirelson (talk | contribs) (More or less generality: not necessarily of dimension 2 or 3)

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More or less generality

The phrase "In a more general sense, a Euclidean space is a finite-dimensional real vector space" does not sound right. Since a finite dimensional real vector space satisfies the abstract Euclidean axioms, it is less general, not more. The general sense should be that, on adding suitable axioms such as continuity and between-ness to those of Euclid, one obtains a system which more or less characterises the real vector space. Richard Pinch (talk) 20:02, 3 March 2018 (CET)

I guess, "more general" means here "not necessarily of dimension 2 or 3". Axioms of Euclid are too ancient... rather, one uses Hilbert system of axioms or another system that is equivalent to real vector space with inner product in dimensions 2 and 3. Boris Tsirelson (talk) 21:34, 3 March 2018 (CET)
How to Cite This Entry:
Euclidean space. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Euclidean_space&oldid=42902