On Wed, 09 Feb 2011 20:14:19 -0500, Igor Tandetnik <[email protected]>
wrote:
> On 2/9/2011 7:29 PM, Samuel Adam wrote:
[…snip garbage…]
>
> It seems (1, 2) and (2, 1) would result in distinct xk values, thus
> defeating the point of the exercise. It is again possible to insert two
> pairs that differ only in order.
You are right. I’ve now devised two different back-of-the-envelope proofs
that I was trying to achieve the mathematically impossible. (Now watch
this: For strike three, somebody will show that it is not only possible,
but trivial.)
Incidentally, I believe I just provided an unintentional object lesson in
the merit of being just a bit formal sometimes. What I was trying to do
(which may or may not have been obvious to Mr. Tandetnik, et al.) is to
find
k = F(x, y) = F′(y, x)
such that k would retain the information of whether F or F′ was used.
Q.E.D. (and affix palm to forehead).
On the bright side, this bungling on my part led me into an interesting
general problem with sets and permutations. That’s not topical, however,
as I have already showed for Mr. Black’s purpose that extra information
cannot be stored in k without breaking the equality. Plus as I’ve said
before[1] and yesterday quite well demonstrated, I am bad at math.
Very truly,
Samuel Adam ◊ <http://certifound.com/>
763 Montgomery Road ◊ Hillsborough, NJ 08844-1304 ◊ United States
Legal advice from a non-lawyer: “If you are sued, don’t do what the
Supreme Court of New Jersey, its agents, and its officers did.”
http://www.youtube.com/watch?v=iT2hEwBfU1g
[1] http://www.mail-archive.com/[email protected]/msg56438.html
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