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

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Hetware

Posts: 148
Registered: 4/13/13
Re: Proof that mixed partials commute.
Posted: Nov 20, 2013 11:26 PM
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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/ .





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