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Fifith Postulate in Affine Spaces

  1. Aug 22, 2006 #1
    If possible, could anyone criticize the following sequence of sentences ?
    1) Two n-dimensional affine subspaces are parallel iff they have the
    same associated linear space.
    2) Two different (non-equal) parallel affine subspaces are disjoint sets.
    3) If two n-dimensional affine subspaces ( 'A' and 'B' ) are parallel to a third n-dimensional subspace then they are parallel to each other. (A || B )
    4) Euclid's Fifth Postulate: Based on item 3), if two n-dimensional subspaces ( 'A' and 'B' ) parallel to a third n-dimensional subspace have a point in common, then they are equal (A = B).
    5) Based on item 4), every affine space obeys the parallel postulate. :confused:

    My question is : What item is wrong ?
    thanx in advance
    Last edited: Aug 22, 2006
  2. jcsd
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