A Lipschitz Proof

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1. Jul 6, 2016

JasMath33

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.

2. Jul 6, 2016

Staff: Mentor

Looks ok to me. What does make you think it might be incorrect?

3. Jul 6, 2016

JasMath33

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.

4. Jul 6, 2016

Staff: Mentor

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.

5. Jul 6, 2016

JasMath33

Yeah I see what you are saying now. It makes sense. Thanks.