Ordering a Line in a Pasch Plane (ORD)

Edward John Specht, Harold Trainer Jones, Keith G. Calkins and Donald H. Rhoads
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Edward John Specht: Indiana University South Bend
Harold Trainer Jones: Andrews University
Keith G. Calkins: Ferris State University
Donald H. Rhoads: Andrews University

Chapter Chapter 6 in Euclidean Geometry and its Subgeometries, 2015, pp 139-148 from Springer

Abstract: Abstract This chapter defines order relations on lines and derives their properties, including transitivity and trichotomy. The concepts of maximum, minimum, upper bound, and lower bound of a subset of an ordered line are developed, as well as the connections between order, segments, and rays. Ordering will assume great importance in later chapters which develop the correspondence between a line and the set of all rational (or real) numbers.

Keywords: Trichotomy; Non-vertical Line; Logical Precision; Earlier Theorem; Numerical Sense (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-23775-6_6

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DOI: 10.1007/978-3-319-23775-6_6

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