Constructive and Non-constructive Methods in Mathematics

  • A. Gardiner


In the previous chapter we started by tacitly assuming that any given pair of line segments could necessarily be measured exactly by some (suitably small) common measure. But, when this assumption was applied to the pair of segments AB, AC in Figure 6, we derived a contradiction. We were thus forced by the principles of logic to admit that our tacit assumption was untenable: there clearly exist some pairs of segments (such as AB, AC in Figure 6) which have no common measure at all.


Line Segment Prime Number Common Measure Remarkable Fact Previous Chapter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • A. Gardiner
    • 1
  1. 1.Department of MathematicsUniversity of BirminghamBirminghamEngland

Personalised recommendations