MATH 2360Q Lecture Notes - Lecture 2: Cartesian Coordinate System, Logical Biconditional, Finite Geometry
Document Summary
An axiomatic system is a collection of undefined terms, definitions, axioms, theorems, and proofs. Rather than defining exactly what a point or line is, we will leave them undefined. Axioms will tell us what these undefined terms need to do. Don"t care what they are, just how they work. Allow us to be less wordy ( collinear rather than all lying on a line ) All other results follow logically from these axioms. We can"t refer to results which are obvious from planar geometry unless they follow from one of these axioms. The axioms are our basic tools (hammer, screwdriver) The undefined terms are the building materials (nails, wood) Theorems (or propositions or lemmas or corollaries) Proofs of each theorem can rely only on the axioms and previously proven theorems. Theorems are the things we can build using our basic tools and building materials. Some of them may even be used to help us build other theorems.
