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Additional problems for HW #14
 
  1. Show if A*B*C and B*C*D, then
    1. A*B*D. (Hint: use the Line Separation Property.)
    2. A*C*D.
  2. Compare the above problem with problem 5 of Section 1.2. They are not the same. There is one more "case" or "type" of "betweenness lemma" we haven't proved yet. What is it?
  3.  
    1. Prove that a circle cannot meet a line in more than two points. Hint: Use the Elementary Principle of Continuity.
    2. Rewrite Step 1 of Construction 5 on page 64, and use part a. above to justify it.
  4. Without using the Elementary Principle of Continuity, prove that a circle cannot meet a line in more than two points. Hint: use Corollary 1.5.12 and Proposition 1.6.4.
Updated: 31 August, 2009 17:44:19