06/05/2014, 10:29 PM
(06/05/2014, 06:51 PM)jaydfox Wrote: I feel like Tommy sometimes (in a good way, I hope he takes this as a compliment). I feel like sometimes I can intuitively see what's going on, but I lack the rigorous mathematical tools to either "prove" what I believe intuitively, or to be able to put my intuition to work. (I see Tommy complaining a lot about people going back to Cauchy integrals, and I can understand his frustration. I'm still a newb with Cauchy integrals myself.)
I guess the compliment is that I have " intuition " or something.
So euh thanks or something.
But what you say about Cauchy is - I think - actually the other way around.
That is too say , people use Cauchy type ideas that are not as formal as they think it is.
They lack proof rather than me.
Just because some integrals are equal to 0 does not imply a function is analytic.
In other words they turn the theorems " upside down " and other handwaving stuff.
My opinion is subtle :
1) I believe in the uniqueness and existance
2) I do not believe in the computation , the method does not work
3) Im not sure completely sure about 2) or if this sexp is a new one. but I need evidence and claim there is none.
The impression that I leave might be unbalanced in the sense that I post and tend not to delete stuff like half-baked ideas or even mistakes.
I do not " polish " my math or ideas.
I hand in the " rough draft " at the exam.
I do not " believe in hiding and forgetting mistakes ".
Quite the opposite actually.
This is a forum and not a paper.
If you know what I mean.
Sometimes I wonder if teachers should point out mistakes they made themselves more often to students.
On the other hand , I suspect they " warn for often made mistakes due to students " which were actually mistakes they (once) made themselves , but that sounds better.
Although one does not exclude the other.
Anyway I did not feel I could not " follow up " the Cauchy ideas , but rather my arguments against the method were not so well understood by the majority.
Despite being skeptical , I still mention Cauchy's method because once again they did compute something ! And there has been no proof for either the optimists or pessimists.
regards
tommy1729

