Finite Geometry Axiom system 1:
There exists a set of objects called Things
There exists another set of objects called Bunches. Each Bunch is a set that includes some Things.
If there is a Thing and a Bunch then either the Thing is in the Bunch or the Thing is not in the Bunch.
- For every two distinct Things there is exactly one Bunch that contains both of them
- Any time there is a Bunch, and a Thing that is not in that Bunch,
then there is another Bunch that contains the thing, and does not
intersect with the first Bunch.
- There exist at least 4 Things where no three of those Things are in the same Bunch.
Task: come up with a way of drawing "Things" and "Bunches" and draw an
example that fits these axioms. What is the smallest number of
Things and Bunches that fit these rules?