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JasMath33
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I was reading this book yesterday and looking at this proof/justification. I was thinking it is possibly incorrect, but wanted to get some other opinions. Here is the example they gave in the book with the work attached.
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:
The evidence supporting this proof will vary depending on the specific proof being discussed. It could include experimental data, mathematical calculations, or logical reasoning.
To ensure the validity and reliability of a proof, it should be subject to peer review by other experts in the field. This involves critically evaluating the evidence, assumptions, and logic used in the proof. Replication of the results by other researchers can also help to confirm its validity.
Like any scientific work, a proof may have limitations or weaknesses. These could include assumptions that may not hold true in all cases, potential bias in the data or analysis, or incomplete understanding of the underlying phenomenon. It is important to critically evaluate these limitations to determine the strength of the proof.
The purpose of a proof is to provide evidence or reasoning to support a claim or theory. Therefore, a valid and reliable proof can contribute to our understanding of a topic by providing new insights, confirming previous findings, or challenging existing beliefs.
In scientific discussions, it is important to consider alternative explanations or counterarguments to a proof. This helps to evaluate the strength of the evidence and identify potential flaws or limitations. It also allows for further investigation and refinement of the proof.