Axiomatization by Means of Coordinates

Erwin Engeler
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Erwin Engeler: ETH-Zentrum, Mathematikdepartment

Chapter § 2 in Foundations of Mathematics, 1993, pp 45-53 from Springer

Abstract: Abstract Since we have imposed on Euclidean Geometry the duty of using the field R of real numbers as distance system, this is easiest to understand as a twodimensional vector space ε over ℝ. With the help of the scalar product the distance function is defined to be $$\left\| {x,y} \right\| = \sqrt {\left( {x - y} \right)\left( {x - y} \right)} $$ for arbitrary x,y ∈ ε.

Date: 1993
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DOI: 10.1007/978-3-642-78052-3_7

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