
The axioms to be used in this paper are, with only two exceptions, the same as those for abstract Euclidean vector spaces. We denote the elements by small letters and call them points. The null element 0, however, will not be considered a point. Capital letters will be used for scalars which are assumed to be real numbers. For addition and scalar multiplication we postulate the usual properties [1, pp. 3-4]. Our axioms for the "inner product," also a real number, are as follows:
foundations of geometry, noneuclidean geometry
foundations of geometry, noneuclidean geometry
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