Ants and paths system axioms:


Axiom 1.  Every ant has at least two paths.
Axiom 2.  Every path has at least two ants.
Axiom 3.  There exists at least one ant.

Questions solved in class:
  1. What are the undefined terms?
  2. Theorem 1: There exists at least one path. Prove it.
  3. What is the minimum number of paths? Justify it.
  4. Show the axioms are independent.
  5. Explain why the system is likely consistent.
  6. Explain why the system is not complete.
You can see hints and solutions on Timothy Peil's website:
http://web.mnstate.edu/peil/geometry/C1AxiomSystem/AxSysWorksheet.htm