Fifith Postulate in Affine Spaces

## Primary tabs

# Fifith Postulate in Affine Spaces

Submitted by rdabra on Tue, 08/22/2006 - 17:56

Forums:

If possible, could anyone criticize the following sequence of sentences ?

1) Affine subspaces are parallel iff they have the same associated linear spaces.

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

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections