Re: Algebra with Q(pi).

Tonico <Tonicopm@xxxxxxxxx> writes:
On Aug 7, 4:22 am, BD <w...@xxxxxxxxxxxxxxxxxx> wrote:
Tonico <Tonic...@xxxxxxxxx> wrote:
On Aug 6, 8:14?pm, BD <w...@xxxxxxxxxxxxxxxxx> wrote:
Jose Antonio Perez aka Tonio aka Tonico <Tonic...@xxxxxxxxx> wrote:
On Aug 6, 6:12 pm, BD <w...@xxxxxxxxxxxxxxxxxxxx> wrote:
Tonico <Tonic...@xxxxxxxxx> wrote:
On Aug 6, 3:49?pm, "mina_world" <mina_wo...@xxxxxxxxxxx> wrote:

[Q(pi) : Q( pi + (1/pi) )] = ?

Put $ = Pi and r = $ + 1/$ ==> $r = $^2 + 1 ==> $^2 - r$ + 1 = 0 ==>
Pi = $ is a root of f(x) = x^2 - rx + 1, with r = $ + 1/$.
If f is reducible then $ belongs to Q($ + 1/$) ==> $ = f(T)/g(T),
with f,g rational polynomials (which we can assume have no common non-
trivial divisors), and T = $ + 1/$ ==> $g(T) - f(T) = 0, and
multiplying through by $ we get that $ is algebraic over Q...

So f is irreducible and then [Q(pi) : Q( pi + (1/pi) )] = 2
. . . or I am wrong, of course.

As usual, you're "wrong, of course", since you failed to rule out the
possibility that h(r) = $ g - f = 0 -- which is the crux of the matter.

As usual you love to make an ass of yourself since I did not rule out
that possibility but left it to the OP for checking it out.

If anyone believes that then I have a bridge I can sell them.
Your reply treated only the most trivial aspect of the problem
Nowhere did you say nor imply that the crux of the matter was
left untreated. Clearly that is because you did not know that.
Indeed, by now there is in fact another followup to your post
which states essentially the same criticism as I.

You seem to have forgotten (the age...**sigh**)
that I don't usually give away compelte answers.

No, I have not forgotten that almost all your "proofs" are wrong.
But I'm glad to see that you are now again warning readers about
your errors by saying things like "... or I am wrong of course"
as you did on many occasions in the past. For many examples see
http://google.com/group/sci.math/msg/28e7b46256e82fc4
http://google.com/groups?selm=y8z63rddi4q.fsf%40nestle.csail.mit.edu

Wow Willy! You posted links...to your OWN posts to support YOUR
nonsense?! Great doing, my boy: huge.

More attempts to hide the truth. The above linked post does indeed
contain links to Tonio's numerous posts where he confesses to his
many errors. Here is a random sample extracted from said post:
+=====================================================================+
| Excerpts from sci.math posts of Jose Antonio Perez = Tonico = Tonio |
+=====================================================================+
Perhaps I missed something here...Sorry, I completely misunderstood
... Indeed it was pretty elementary [1]http://tinyurl.com/57uvgp

It may well be I misunderstood some things [2]http://tinyurl.com/6fremu

I may be missing something basic here [3]http://tinyurl.com/59qvkn

I may be missing something here [4]http://tinyurl.com/67wg4h

I was TOO missing something [5]http://tinyurl.com/5tztwy

As usual I may be missing something [6]http://tinyurl.com/59md5s

That was a stupid mistake I made up there [7]http://tinyurl.com/5k28xf
+-----------------------------------------------------------------------+
etc. Those are just a sample of the posts where Tonio realized a priori
that he probably made an error. There are an order of magnitude more posts
where he makes significant errors and doesn't even realize it in advance.
I will spare him the embarrassment of listing every one of those here.

And a propo "examples", what about the next few ones that show your
"high" discussing level with people?:http://tinyurl.com/lsu9ba
And what about the next one where you cowardly (as usual, what else is
new?) attack me (yay, you're bad boy!) of some nonsense in a thread
which I didn't even take part in?
http://tinyurl.com/http-at-yorku-ca-cgi-bin-bbq
Hey, following the same flavour as the above ones:
http://tinyurl.com/http-at-yorku-ca-cgi-bin-bbq
All these show how you're fond of getting into nonsensical, futile and
childish discussions with beginner students about NONSENSICAL points
in definitions, which have no real specific weight in the true
development of mathematicians.

Duh, you gave 3 links to the same post - one that does nothing at all
to support your vacuous claims. Indeed, if you read that post carefully
(which I know is asking too much of you) you will see that Kris make a
mistake - he misattributed to BD some foolish remarks made by ".//."
But ".//." is, of course, the anonymous coward Tonio. So Kris is actually
arguing with you, not me. How ironic, you've actually insulted yourself,
just as you did in all the warnings announcing your errors that I cited
at length above. Great job Tonio! You earned this: lim *PLONK*^n, n->oo

[0] http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist;task=show_msg;msg=1827.0001.0001.0001.0001.0002.0002.0001
[1] http://google.com/groups?selm=1160046334.164177.156020%40m73g2000cwd.googlegroups.com
[2] http://google.com/groups?selm=5a00aded-ee32-466b-8435-3487e5b60031%4079g2000hsk.googlegroups.com
[3] http://google.com/groups?selm=1162980604.054697.109000%40m7g2000cwm.googlegroups.com
[4] http://google.com/groups?selm=1160137528.705982.23500%40i42g2000cwa.googlegroups.com
[5] http://google.com/groups?selm=1105865041.950427.117800%40f14g2000cwb.googlegroups.com
[6] http://google.com/groups?selm=1163580175.548902.280950%40m7g2000cwm.googlegroups.com
[7] http://google.com/groups?selm=8c09f9d2.0401290226.43dc72ae%40posting.google.com

*Giggle* It must be cosy in your tiny, little world Bill. No wonder...

Oh, and I bet you can prove ..//. or whatever is me just as I can
prove that you're the coward anonymous who posted the next pearls:
http://tinyurl.com/mjhera
Beginning from the post's title: the same style, the same cursing
you've used before ("patheticexcuse of human being, etc.)....
ah, Wall-e...erm, Willy: you naughty boy!
You really made a point in good taste and high level in those post,

Typical crank: you lost the above argument so now you're shifting
to another argument - this even more hopeless than the former.
I supplied links to many posts of yours that support my claims.
But the best you can do is link to some random anonymous post,
nothing like anything I have ever written and, and make the
completely outrageous claim that I authored it. Get a clue:
if you Google the above phrase you will find that it is a
common English idiom (> 3 million hits). With all the people
you've bashed here over the years, I can imagine hundreds
if not thousands of possible authors of such a post.
.

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