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Topic: Proof that mixed partials commute.
Replies: 20   Last Post: Nov 22, 2013 11:57 PM

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Robin Chapman

Posts: 297
Registered: 5/29/08
Re: Proof that mixed partials commute.
Posted: Nov 20, 2013 11:25 AM
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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!).



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