Kindly comments on Mental Context for Model Theory - Less Wrong
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Comments (45)
I'm not sure why this comment is being downvoted - perhaps because of the tone - but the content in it is true
The definition of parallel lines is essentially "lines that don't intersect". We therefore do not need an axiom to show that if two lines are parallel, the do not intersect - this just follows from the definition.
The fifth postulate says that for every line L and point P outside of L, the parallel line L' through P is unique (Existence of L' follows from axioms 1 through 4)
This: