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:
- What are the undefined terms?
- Theorem 1: There exists at least one path. Prove it.
- What is the minimum number of paths? Justify it.
- Show the axioms are independent.
- Explain why the system is likely consistent.
- 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