CIS 1910 Lecture Notes - Lecture 7: List Of Theorems, Contraposition

• School: University of Guelph
• Department: Computing and Information Science
• Course: CIS 1910
• Professor: Luiza Antonie

Document Summary

A theorem is a statement that can be proven to be true. A proof is a valid argument that establishes the truth of a theorem. A proof consists of a series of steps, each of which follows logically from assumptions, or from previously proven statements, whose final step should result in the statement of the theorem being proven. A proof may use: hypotheses, axioms, previously proven theorems, lemmas, corollaries, rules of inference in the final step of the proof, you establish the truth of the statement to be proved. Fortunately, many proofs follow one of a relatively small number of patterns. Coming up with proofs requires trial and error, even for experienced mathematicians. Often the process includes experimenting with small examples in order to develop intuition about a more general rule. The process almost always entails some dead ends along the way. Before proving a theorem, it is essential to understand exactly what the theorem is saying.