proof

proof in mathematics, finite sequence of propositions each of which is either an axiom or follows from preceding propositions by one of the rules of logical inference (see symbolic logic ). Mathematical proofs are quite distinct from inductive, statistical, heuristic, analogical, and other types of reasoning or persuasion that are sometimes accepted as proofs in other fields of science or human affairs. Proof theory has developed into one of the important branches of modern mathematical logic. Some schools of mathematical logic reject certain methods in proofs, such as use of the law of excluded middle (either p is true or p is false) or of mathematical definitions involving properties that are not effectively verifiable.

proof adj. able to withstand something damaging; resistant: the hardened walls were proof against most weapons.

proof the proof of the pudding is in the eating proverbial saying, early 14th century, meaning that the truth of an assertion will be demonstrated by how things actually turn out; proof here means ‘test’ rather than the more normal ‘verification, proving to be true.’

See also burden of proof.