Final answer:
A proof is designed to verify a theorem by providing logical justification and evidence. It involves a series of logical steps starting from axioms, other theorems, and definitions to conclude the truth of the proposed theorem.
Step-by-step explanation:
A proof is a series of steps, with justifications, that verifies a theorem. The goal of a proof is to establish the truth of a mathematical statement, which has already been proposed as a theorem, by logically deriving conclusions from a set of axioms, definitions, previously established theorems, and logical reasoning. Proofs are an essential aspect of mathematical logic and are used to ensure the validity of a theorem. In contrast, a postulate (or axiom) is a statement that is assumed to be true without proof, a counterexample is an example that disproves a statement or proposition, and a definition merely explains the meaning of a term without requiring proof.