Re: Bring Math Arguments against this FERMAT LAST THEOREM PROOF

On 29 Aug 2005 13:19:29 -0700, matt271829-news@xxxxxxxxxxx wrote:

>
>quasi wrote:
>
>[snip]
>
>>
>> Yes, that would fix things, but now you are trying to repair his proof
>> for him. Why not let him do that? I would stop at the first place
>> where things are unclear and object or ask for clarification rather
>> than trying to push on.
>
>He has a history of being unable to respond clearly to simple
>questions, so the idea is that the more help and leading you give him
>the more chance there is of getting a straight answer. (Having said
>that, I am not sure that this has actually been borne out in practice.)

Ok, but the objection is very simple, so it needs to be addressed.

To George:

The case Z is not a multiple of 3 does not force X to also not be a
multiple of 3, so if you want all the variables X,Y,Z to be not
multiples of 3, then you have to say so. Thus the 2 cases would be:

(1) X,Y,Z are not multiples of 3 (or X*Y*Z not a multiple of 3)

(2) exactly one of X,Y,Z is a multiple of 3.

Now, If X,Y,Z are assumed to be positive integers, then case (2)
splits into 2 subcases:

(2z) Z is a multiple of 3 but X,Y are not multiples of 3.
(2x) X is a multiple of 3 but Y,Z are not multiples of 3.

The reason we need 2 subcases, even though they appear to be nearly
the same, is the lack of symmetry in the equation X^3+Y^3=Z^3.

Z is clearly larger than both X,Y and those inequalities might be
later invoked as part of the proof. Note that at this point, X,Y are
symmetric so we don't need 3 subcases, however if at some point you
assume X<=Y, then that symmetry would also be broken, and then you
would need 3 subcases instead of 2 (awkward and ugly!).

So if no inequality assumptions comparing X,Y,Z are used in the proof,
then it's better to symmetrize the equation at the outset, writing it
in the form X^3+Y^3+Z^3=0, so as not to have to deal with subcases
which are similar but not exactly the same.

Ok, George, so here's the deal. If you want to play this game, you
need to be willing to either defend against an objection by explaining
why it's not legitimate, or else deal with the objection by repairing
the proof.

quasi
.

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