In mathematics, the statement of an exercise is typically the same as that of a lemma, proposition or theorem, but the attitude towards its proof is different:
An exercise is for the reader to fill in a proof, in private. The reader may seek help from whomever, but the idea is to practice. A great many exercises have been publicly solved, and a great many theorems have not, thus confusing which are which, though it’s generally good practice to treat them all as exercises and ignore published proofs, within the constraints of available time and balancing of competing priorities.
When a proposition is called an exercise, this means at least that the omission of a proof is deliberate (or that its inclusion is accidental), but the author is confident of being able to produce one, given enough patience.
mathematical statements
Last revised on March 5, 2023 at 13:36:19. See the history of this page for a list of all contributions to it.