Hetware
Posts:
148
Registered:
4/13/13


Re: Proof that mixed partials commute.
Posted:
Nov 20, 2013 11:26 PM


On 11/20/2013 11:25 AM, Robin Chapman wrote: > On 20/11/2013 11:55, Hetware wrote: >> On 11/20/2013 3:22 AM, Robin Chapman wrote: > > The 11th of WHAT? > >>> On 19/11/2013 23:59, Hetware wrote: >>> Of course there are examples where mixed partials are different, >>> so your original argument can't have been valid, since it didn't >>> use the necessary hypotheses about continuity of partials etc. >>> >> >> But I added my reason for assuming the limits commute. I expressed a >> function of two independent variables as the function of a single >> variable and appealed to the limit rules for a function of a single >> variable to the result. >> >> The question is whether that reasoning is valid. > > I found your original post unreadable, in part due to > the wilfully obscure notation, but also due to your > vagueness of quantification.
I prefer to think of my notation as concise, if a bit cryptic; relying on the intuition of the reader to flesh out the full meaning.
But as I pointed out, > your argument couldn't have been valid as it failed to > use some necessary hypotheses. I can't see any value > in trying to parse your argument in detail trying to > find the first error; if you had written it in decent > mathematical English, I might have had a go (and you might > have noticed any errors yourself!).
There were no errors on my part. Other than a reversal of xy as a subscript. If you follow my exposition, you will have wisdom. Be grateful.
Fact of the matter is, I cannot communicate well in ASCII. I can express ideas very tightly with the proper symbols. But I am not Kosher enough to communicate on such fora as http://www.physicsforums.com/ .

