Final answer:
A formal proof in mathematics uses theorems, geometry rules, and algebra rules, but not a set of examples, as examples alone do not constitute a formal proof.
Step-by-step explanation:
A formal proof in mathematics involves a logical sequence of statements that lead to a conclusion based on deductive reasoning. This process often relies on using theorems, geometry rules, and algebra rules to support our assertions. However, formal proofs do not typically include a set of examples as a means to establish or verify the proof - examples may illustrate a principle, but they do not constitute a formal proof. Formal proof methods are an application of logic, geometry, and algebra to demonstrate the truth of statements with certainty, assuming the postulates and rules applied are correct.