Attack of the Hyper Kimmy....

[Scellanis]

Thats the same axiom...just worded differently and given a different number. As you can see my axioms are defined to be easier to understand....no doubt the quote Alice has is from a maths text book where they use fancier language and make more rigorous (and confusing) definitions.

[ganymede]

YEEAAAAAGH!!!!! maths!!! head for the hills!!!!!

[Gwared]

Hee hee - both places are on the same finite affine plane of thought. By the way, did you and the person Alice found both change your minds half-way through the explanations, or am I just totally not getting it?

Axiom 1: There exist at least four points no three of which are collinear.

2. There are 4 distinct points in P, no 3 of which lie together on the same line.

Another way of wording the question that explains the confusion is;

"There exist at least 4 points, from which no 3 are co-linear" i.e a maximum of two can be on the same line (if I remember correctly...it's been over 6 years since I did any maths other than statistics).