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Ordering a Line in a Pasch Plane (ORD)

In: Euclidean Geometry and its Subgeometries

Author

Listed:
  • Edward John Specht

    (Indiana University South Bend)

  • Harold Trainer Jones

    (Andrews University)

  • Keith G. Calkins

    (Ferris State University)

  • Donald H. Rhoads

    (Andrews University)

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.

Suggested Citation

  • Edward John Specht & Harold Trainer Jones & Keith G. Calkins & Donald H. Rhoads, 2015. "Ordering a Line in a Pasch Plane (ORD)," Springer Books, in: Euclidean Geometry and its Subgeometries, edition 1, chapter 0, pages 139-148, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-23775-6_6
    DOI: 10.1007/978-3-319-23775-6_6
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