math+drinking=fun!
For Universal Geometry, we had to apply geometric axioms to life by replacing the words point, line and plane with some other system. So, here's my homework.
I1: For any two distinct drinkers, there is at least one conversation incident to them.
I2: For any two distinct drinkers, there is at most one conversation incident to them.
non-I2: Some pairs of drinkers have more than one line incident to them. (This is for spherical geometry, in the case of antipolar drinkers)
I3: Each conversation contains at least 2 drinkers (for planar geometry)
3 drinkers (for projective geometry)
(This one doesn’t work as well, because I’ve recently learned that there are also conversations between non-drinking people.)
I4: Not all drinkers are in the same conversation.
I5: For any distinct drinkers Adam, Brad and Chad, there is a college party α, incident to them.
I6: For any distinct drinkers Adam, Brad and Chad, there is at most one party α incident to them.
(This axiom also doesn’t really work given the vast quantity of parties and small student body at Chapman.)
I7: Given party α and drinkers Adam and Brad incident to party α, the conversation Adam-Brad is incident to α.
I8: If 2 parties α and β are incident to a drinker Adam, then there is at least one drinker Brad, distinct from Adam, who is also incident to α and β.
I9: Not all drinkers are co-partiers.