The discussion revolves around the correctness of a proof related to Lipschitz continuity presented in a book. Participants are examining the clarity and completeness of the proof, particularly focusing on the ending and whether it adequately conveys the conclusion that a function is Lipschitz continuous.
Participants do not reach a consensus on the correctness of the proof. While some find it acceptable, others express uncertainty about its completeness, indicating a lack of agreement on the matter.
The discussion highlights potential assumptions about familiarity with Lipschitz continuity and the expectations for mathematical proofs, which may not be universally shared among participants.
I guess what threw me off was the ending. I was just expecting to see something stating therefore the the function is Lipschitz. I guess in the book, they wanted you to just in your head think that.fresh_42 said:
Well, it's the definition of Lipschitz continuity. If one has to show a number ##n## is even and shows it is divisible by ##2##, nobody would complain about a missing "... therefore ##n## is even", because we are used to the concept of even numbers. It is the same here: simply a matter of acquaintance. Maybe it would be a little more obvious if one had chosen ##L## instead of ##M## as the constant.JasMath33 said:
Yeah I see what you are saying now. It makes sense. Thanks.fresh_42 said: