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Rational Points on a Line (QX)

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 is concerned with an arbitrary line in a Euclidean plane, where this line has been built into an ordered field. It defines the meaning of a rational multiple of a point on this line, develops the arithmetical properties of such multiples, and uses these to show the existence of an order-preserving isomorphism between the set of all rational numbers and a subset of the line.

Suggested Citation

  • Edward John Specht & Harold Trainer Jones & Keith G. Calkins & Donald H. Rhoads, 2015. "Rational Points on a Line (QX)," Springer Books, in: Euclidean Geometry and its Subgeometries, edition 1, chapter 0, pages 347-359, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-23775-6_17
    DOI: 10.1007/978-3-319-23775-6_17
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