mm-2199
Not really. It happens not infrequently that 0 is a counterexample to
some stated result. If 0 is the only counterexample, then this is not
particularly interesting.
Derek Holt.
can be corrected simply 
Hum, I think I get the idea. If 0 is the only counterexample, a
simple condition (x =/= 0) may patch the argument, right? While,
if there's many x which are counterexample, then the argument may
be simply flawed. Is that what you mean?
Hello all,
http://www.maa.org/editorial/mathgames/mathgames_02-14-05.html you
might be interested in this:
On Keen Approximations,
http://www.geocities.com/titus_piezas/Approximations.htm
measure of their keenness, the highest of which had a score of
2.381.
However, we can improve on this using class polynomials, the highest
-Titus
(tpiezas@uap.edu.ph)
That's interesting, because my experience has been
that a published mathematical result is given no
weight by those outside of mathematics [1], and
substantial weight by those in mathematics. I will
admit that experts in the paper's specific field
are probably not going to assign much additional
weight for its publication, since they've all
known of it for a couple of years from conference
announcements, others already applying the result,
availability of preprints, etc. However, when you
include the 99.8% of the remaining mathematicians
(not to mention hiring and promotion committees),
publication is critical since otherwise how can
you consider the things that really matter, such
as journal quality, page count, its Science
Citation Index rank, etc.?
[1] I realize that those outside of mathematics
    aren't going to give any weight to a
    non-published mathematical result either.
    However, these two observations imply that
    there is a 10,000% increase in the weight
    given by those outside of mathematics to a
    published result over an unpublished result.
Dave L. Renfro
P.S. The humor-impaired are hereby notified that this
     post was intended to be tongue-partly-in-cheek.
Shutup idiot... 
That is true. Mathematics is a human endevour. 
Rejected again?
--
There are two things you must never attempt to prove: the unprovable -- and
the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
toss
hostile
You misspellede sensible.
Yes, a reputation as an .86berkrank...
No, you brain fart.
No, making over-the-top bogus claims without proof is not part of 
brainstorming.
No kidding...
I am hapy with the way you use Usenet.
Nice mixed metaphor! Keep it up...
Yes, that is why you have never published, except for a very short abortion 

that got yanked.
Read: I make wild guesses about the properties of quantities about which I
have no knowledge whatsoever. Then I proclaim that these guesses are
provable and so simple even a child can grasp them.
You have already revealed more about yourself than you have about
mathematics. Note that there is (again!) no math in your post.
That's an inappropriate use of a newsgroup. This isn't a kitchen
refrigerator set up to carry your uncritical Post-Its. It's a *math*
newsgroup, not a *speculation and conspiracy theory* newsgroup. Unproven
ideas are welcome, but flinging loaded diapers is not.The record shows that
your ideas are predominantly wrong, and that your character is terminally
flawed. And observe that you forfeit your right to free speech whenever you
attack others for exercising theirs.
Very profound. May we quote you?
Billy the Barnacle
--
There are two things you must never attempt to prove: the unprovable -- and
the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
No, this is not a clear statement of what you do.
What you do is toss out ideas, calling them proofs. You toss
out assertions that you couldn't prove in a million years, announcing
that you've proved them, and then you explain that anyone who
says you're wrong is either lying or saying that Math Itself is
wrong.
There's a teensy difference between that and just tossing out
ideas.
Nope.
Yes, I can be a rational adult and believe all that.
Have you heard from the Annals yet?
************************
David C. Ullrich
Routinely every couple of years or so I explain my brainstorming
process, about how I put up a lot of ideas expecting most of them to
flop over and die, and having explained it recently, it's also time I
think for me to be reasonable when it comes to the realities of certain
newsgroups.
I can create threads night and day on sci.math and it doesn't matter as
there is a lot of posting volume there, but it really is intrusive I
think to create a lot of threads on newsgroups where there is less
thread generation activity.
So I will curtail the thread creation on all newsgroups except for high
volume ones, so that means a drop in new threads, after this one, on
sci.crypt, alt.math.recreational, and alt.math.undergrad, as I think
that it can be a bit much on low volume newsgroups to create a lot of
threads.
BUT a poster has the right to do so as it IS Usenet.
And don't forget that it is Usenet.
I'm choosing to be less obtrusive on certain newsgroups, but remember,
reading is a choice, so even if there are a lot of threads from a
particular person, you can just choose to ignore them, like there are
all these television channels that I routinely choose to ignore, though
I flip past them while channel surfing.
I never get the urge to contact the distribution outlets and berate
them for putting up all this content that I don't want to see.  I also
don't presume that I can speak for millions of other people by deciding
that what I don't want to see, no one else would want to see.
I don't get an arrogant attitude where I decide to myself that I can
represent everyperson to decide what content is worth putting out
there, and what should just be censored and never seen or heard.
Don't like someone's postings?  Turn the channel.
James Harri
Don't forget to take your own advice too James. You are often very
outspoken against those who respond to your thread when you're
perfectly capable of ignoring them as well. One of the points of
newsgroups is that even the harshest critic is allowed to express
their opinions of your work. Just remember that this gives the
discerning reader the ability to make up their own mind as to who to
listen to and who to ignore. It never hurts to give others the same
respects you expect for yourself even when they don't neccesarily
deserve it.
        You are brainstormed indeed, in the British sense.
So does everyone else. But the expectations of others, which generally turn
out to be true, are expressed by doubts about your unsupported claims. You
claim to have proofs when you don't.
OK. Don't *you* forget that newsgroups are topical, and off-topic posts are
unwelcome. So are cranks and trolls.
If you turned to a technology channel and only found weeping and wailing
there you might be offended. If some crank kept grabbing the mike it is
reasonable to resent his use of limited air-time.
You also don't honor the purported purpose of topical newsgroups, as you
post all kinds of personal issues in technical forums.
No, you're just arrogant about your own behavior. A pattern of worthless,
hostile posts is sufficient to identify a poster as a crank. Most
newsgroups abhor cranks. But, no one has censored you. (If you believe
otherwise, post your evidence.)
Can't post on-topic material? Change the newsgroup.
--
There are two things you must never attempt to prove: the unprovable -- and
the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
 But does it need
Well, you need a discontinuity in the second derivative. Loosely
speaking, most combinations of the elementary functions and their
derivatives are continuous most places -- discontinuities occur when
denominators are zero or where piecewise defined functions don't match
up (and other possibilities). So if you are going to have a
discontinuity using a nice formula, you are probably going to have a
0 in the denominator and a 0 in the numerator with the function being
defined at that point separately. Having said that, I am not claiming
that these types of functions are the only ones to fail Clairaut's
conditions. They are certainly where to look.
--Lynn
I beg to differ:
f_xy is normally written with the @ symbol  (@/@y) ( @f/@x) with the y
to the left of the x and in the shorter form @^2 f / @y @x because the
@ is a left hand operator.
--Lynn