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. 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!).