A mathematical proof is an argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems, along with the accepted rules of inference. Proofs establish logical certainty, to be distinguished from empirical arguments which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases.
In this chapter, we cover the rules of inference, as well as the main methods of proof in mathematics logic,
with one exception, inductive proofs that will be covered in the next chapter.
Lecture Notes
Further Reading
