If possible, could anyone criticize the following sequence of sentences ?(adsbygoogle = window.adsbygoogle || []).push({});

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.

My question is : What item is wrong ?

thanx in advance

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# Fifith Postulate in Affine Spaces

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