User talk:EJ

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[edit] Welcome

Hello, welcome to Wikipedia, EJ!!

I hope you like this place and have fun editing.
We always like to meet new Wikipedians! We sure can use someone writing about logic, thanks for your first edit. Here ar some more things to do, in case you're bored. But don't feel pressed by that.

[edit]

Here are some tasks you can do:


You might find these links helpful in creating new pages or helping with the above tasks: How to edit a page, How to write a great article, Naming conventions, Manual of Style. You should read our policies at some point too.

If you want get to know more the people here, list yourself at Wikipedia:New user log, and go back there sometimes to see if you find people matching your intersts. Go to Wikipedia:Community Portal to learn more about wikipedia and ways to participate.

If you have any questions, see the help pages, or add a question to the village pump. You also can leave me a message at User talk:Lady Tenar, but it may take a few days bevore i see the message and can respond.

Here are some more tips:

  • You can sign your name using three tildes, like this: ~~~. If you use four, you can add a datestamp too.
  • If you ever think a page or image should be deleted, please list it at the votes for deletion page. There is also a votes for undeletion page if you want to retrieve something that you think should not have been deleted.

Again, welcome!

Lady Tenar 13:12, 19 Aug 2004 (UTC)

[edit] Edit attributions

Hi EJ. Edits from 147.231.88.135 have now been reattributed to you. Regards — Kate Turner | Talk 03:01, 2004 Sep 4 (UTC)

Thanks! -- EJ 11:25, 7 Sep 2004 (UTC)

[edit] Usercat

You were listed in the Wikipedia:Wikipedians/Czech Republic page as living in or being associated with Czech Republic. As part of the Wikipedia:User categorisation project, these lists are being replaced with user categories. If you would like to add yourself to the category that is replacing the page, please visit Category:Wikipedians in Czech Republic for instructions.Rmky87 07:37, 17 August 2005 (UTC)

[edit] galois theory

Why is Gal(R/Q) trivial? Dmharvey Image:User_dmharvey_sig.png Talk 17:40, 18 August 2005 (UTC)

Sorry, let me rephrase that. Why are there no nontrivial automorphisms of R which fix Q? Dmharvey Image:User_dmharvey_sig.png Talk 17:40, 18 August 2005 (UTC)

R is real-closed, thus every automorphism f of R is order-preserving: if a ≤ b, there is c such that b=a+c2, which implies f(b)=f(a)+(f(c))2, thus f(a) ≤ f(b). As f fixes Q and Q is dense in R, f must fix R as well. (The assumption that f fixes Q is of course redundant, as every automorphism fixes the prime field.) -- EJ 09:42, 19 August 2005 (UTC)
Hey thanks very much, that's very cool. I'll add that to the article in a few days, I don't think it's something that everyone encountering galois theory (like me!) has seen, and otherwise its very difficult to see why the R/Q and C/Q cases so different. Dmharvey Image:User_dmharvey_sig.png Talk 10:47, 19 August 2005 (UTC)

[edit] Regarding the Mathematician Wikipedians category

Hi, it has been suggested that Category:Mathematician Wikipedians be deleted, because it is a duplicate of the more correctly named Category:Wikipedian mathematicians. I would recomend you simply edit your userpage and add yourself to Category:Wikipedian mathematicians (or one of it's sub-categories) instead by adding this to your userpage:

[[Category:Wikipedian mathematicians|{{subst:PAGENAME}}]]

If you disagree your can visit Wikipedia:Categories_for_deletion#Category:Mathematician_Wikipedians and vote against the deletion or just voice your opinion. --Sherool 22:15, 28 August 2005 (UTC)


[edit] list of set theory topics

Hello. If you're interested in set theory, could you help make the list of set theory topics complete? Thanks. Michael Hardy 01:34, 11 September 2005 (UTC)

[edit] Science pearls

Hi,

Please notice the above project. As a mathematician, you might be especially interested in List of publications in mathematics

I’ll appreciate any help. Thank, APH 10:04, 18 September 2005 (UTC)

[edit] Message from Randall Holmes

Dear EJ,

In the alternative set theory article, the description I had in mind was the contrast between "definite" and "indefinite", which is appropriate for the set theories they had listed, as contrasted with ZFC, but not so appropriate for New Foundations and positive set theory, which are certainly also "alternative set theories" in the broadest sense. Your edit is fine with me...

Randall Holmes 15:50, 16 December 2005 (UTC)

If you are referring to the blurb about "discrete or crisp" set theory, I somehow missed when it was added in the article, but it was misguided. "crisp" is a term used only in fuzzy set theory, and it is not meaningful in other contexts (it is not e.g. used in Hajek's theory of semisets). AFAICS "alternative set theory" does not mean much more than "not ZFC (or its simple modification)", so NF perfectly fits the bill. Anyway, I have doubts about usefulness of the alternative set theory article in its present form.
PS: the work you have done on the NF article is wonderful. -- EJ 01:19, 17 December 2005 (UTC)
It's nice to be appreciated. It ought to be wonderful, since I am one of the very few people who thinks about New Foundations (actually, mostly about NFU) professionally. On a similar note I have been contemplating adding real discussion of the axioms and motivation for the Alternative Set Theory to that article, but I note that you may be better qualified to do this. At any rate, if I jump in and do it anyway I rather imagine that my work will be edited... Randall Holmes 00:18, 21 December 2005 (UTC)
Further, is there still a community working on the Alternative Set Theory? Randall Holmes 00:18, 21 December 2005 (UTC)
Sorry for not responding earlier. You can expect your work to be edited, that's how a wiki is supposed to work, and there is nothing wrong about it. If you have an idea how to describe AST in the article, please do it. I was thinking about writing it myself, but apart from lack of time, I don't feel qualified because motivation and "philosophical" background of this theory are fundamental for its understanding. I never cared much about the motivation, and forgot what I had known about it, as I was always more interested in the formal aspects of the theory. So, I could summarize Sochor's axiom system, and write a few words about its proof theoretic properties, but that's about it. Doing just that would seriously misrepresent the theory, and do more harm than good.
Ad community: no, as far as I am aware the subject is dead since late 80's. -- EJ 17:05, 16 January 2006 (UTC)

[edit] Found You!

Please, excuse my haste and joy. You are The english:WP czech - but not referenced by language. Would you mind helping the reference Desk there ? Thanks a lot. --DLL 22:32, 21 January 2006 (UTC)

I'll take a look, but don't hold your breath, it's a quite long text. -- EJ 16:00, 22 January 2006 (UTC)

[edit] Thanks!

Thanks for your help in the traslation! Czech is a definitively difficult language for me, and Internet doesn't have many free automatic traslators. If you need some help, whatever the problem is, ask me! --COA 23:37, 22 January 2006 (UTC)

You're welcome :) -- EJ 05:36, 23 January 2006 (UTC)

[edit] Date links

Since you have taken an interest in links. Please be kind enough to vote for my new bot application to reduce overlinking of dates where they are not part of date preferences. bobblewik 20:33, 25 February 2006 (UTC)

[edit] The theory of algebraically closed fields

Thank you for the explanation and the description of the axioms. I was under the misapprehension that ACF might be able to express all theorems that someone might include in a book about algebraically closed fields, including those in a chapter on fields of characteristic zero. Would it be correct to say that the theory does not deal with the theory of fields of characteristic zero at all, since its theorems are those that are true for all algebraically closed fields? Also perhaps even expressing the concept of a field having characteristic zero in this theory would require an extension to the theory with an infinite number of axioms, or something as strong as Peano's axioms? Elroch 00:04, 16 March 2006 (UTC)

The weakness of ACF is not in missing axioms (like axioms about the characteristic), but in the poor expressive power of its language. Indeed, it is easy to extend ACF by axioms of the form 1 + 1 + 1 + ... + 1 ≠ 0, which express that the characteristic is 0; the resulting theory is usually called ACF0. Even though this sequence of extra axioms is infinite, ACF0 inherits all the nice properties of ACF (such as decidability), and it has a nice feature on its own: ACF0 is complete. This implies, for example, that every first-order sentence true in the field of complex numbers is provable in ACF0.
However, the expressive power of the language of ACF0 is extremely limited. We can express polynomial identities like y = x2 + 1, we may combine them using Boolean connectives, and we can use existential and universal quantifiers running over all elements of the field, and that's all. In fact, the quantifiers do not help here at all: ACF and ACF0 have quantifier elimination, which means that every formula can be rewritten so that it does not use any quantifiers.
Thus, almost nothing from a book about algebraically closed fields of characteristic 0 can be formulated in ACF0. We cannot talk in the theory about subfields, transcendence bases, automorphisms, and similar concepts. And, by the same token, we cannot talk about integer arithmetic. Every algebraically closed field of characteristic 0 contains an isomorphic copy of the integers, and each integer has a "name", but we cannot distinguish between integers and nonintegers by a single formula of ACF0. This means that even simple properties of the integers, like "every integer is either odd or even", cannot be formulated in the language of ACF0.
It's getting too long, so I'd better stop here. Hope this helps. -- EJ 04:13, 16 March 2006 (UTC)
Yes, thanks for the clarification. Elroch 12:09, 16 March 2006 (UTC)

[edit] Are you aware of this Wikipedia talk:Censorship ?

For myself, I would like to say that the method is not innocent. The subject is truly important : there is one talk page and twoscore people discussing auto censorship for one million (counting non active users). Will you give your advice ? --DLL 20:10, 21 March 2006 (UTC)

[edit] Caron/hacek vote

There's a vote on Talk:caron where the article should be if you're interested. +Hexagon1 (talk) 10:06, 26 March 2006 (UTC)

Thanks for the notice. Nevertheless I probably will not vote, as I don't have a clear opinion either way. -- EJ 05:05, 27 March 2006 (UTC)

[edit] Good job on Jordan curve theorem

Hi, I haven't been watching that article, but I noticed that you undid the hype about the Mizar proof. I noticed a while ago (through Usenet) that the author of the link (after the statement in the article) says quite a few misleading statements implying that somehow the Mizar proof is the first "real" proof. I didn't think to check Wikipedia and see if someone would insert this nonsense. Anyway, I just wanted to say nice job, and say that I removed the link with dubious comments; the external links already contain a link to the Mizar proof, and I think it best to avoid an overeager editor from reading the link and putting the stuff back in. --Chan-Ho (Talk) 16:36, 9 April 2006 (UTC)

Thanks for appreciation, and sorry for delayed answer. I also feel uneasy about the way how some of the Mizar people present their result, discrediting the work of Veblen and other mathematicians who proved the theorem. It is cool to have a formalized proof of JCT (albeit in a ridiculously strong set theory), but that's no excuse for twisting the history. -- EJ 18:22, 16 April 2006 (UTC)

[edit] About Euclidean algorithm

Could you explain the revertion [1]? The term atomic operation is the wrong term to be used there, because a machine operation is not considered atomic even if it's a single instruction, see atomic operation. I think you mean either constant time or non-constant time operations. Second, it's more general to specify division complexity with respect to number of digits n so that both software based divisions and constant time machine divisions can be analyzed (machine divisions are always limited range arithmetics O(1) operations). Shd 17:22, 18 June 2006 (UTC)

[edit] your edit to riemann hypothesis

I think the statement as it was written originally is "almost true", in the sense that one can prove that

\limsup_{n \to \infty} \left|\frac{M(x)}{x^{1/2}}\right| = \infty

This is weaker than the Ω statement though, which is certainly false. I don't have a reference for this. I just think I remember seeing it somewhere (i.e. not on wikipedia :-)). Dmharvey 00:56, 25 July 2006 (UTC)

Although I note that the article Merten's conjecture contradicts my claim, so maybe I'm full of crap. Dmharvey 01:00, 25 July 2006 (UTC)
This formula is indeed an unproven conjecture, if I read the article on Merten's conjecture correctly. I also don't have any references on the subject; I simply changed the suspicious
\liminf \left|\frac{M(x)}{x^{1/2}}\right| > 0
to
\limsup \left|\frac{M(x)}{x^{1/2}}\right| > 0,
because I hope that it was intended that way by the author of the original statement. -- EJ 01:29, 25 July 2006 (UTC)

[edit] Matiyasevich's theorem

Hello. Interesting edit. Fortunately, it's not nonsense (although it was after the edit I reverted this morning---someone called the deleted text "unencyclopedic", but his edit changed the meaning). I'll dig out a reference. Do you know any other sexy examples of old-fashioned narrowly-construed Aristotelian syllogisms getting so much attention from mathematicians? Michael Hardy 18:44, 7 September 2006 (UTC)

To the best of my knowledge, the syllogism embodied in the derivation of unsolvability of Hilbert's 10th problem is not getting any attention from mathematicians; I'd guess 99% of mathematicians are not actually aware it is a syllogism, or even do not know what is a syllogism. In any case, syllogisms are very common all over the place. A lot of useful theorems are universal statements like "every compact space is Baire", "every continuous function has the Darboux property", "every finite division ring is commutative", "every bounded entire function is constant", etc. These are typically applied by constructing an object which is compact (continuous, ...), and concluding that the object is a Baire space (Darboux, ...). This kind of argument is a schoolbook application of a Barbara syllogism.
So, I'm eagerly waiting for your references showing that syllogisms are rare in mathematics, and how on earth it is possible to apply a complete triviality like syllogism in a nontrivial way. -- EJ 16:58, 8 September 2006 (UTC)
"syllogisms are very common all over the place"
Yes and no. It is not "common all over the place" for mathematicians to learn and rely on Aristotle's list of valid and invalid syllogisms. As far as "getting attention" is concerned, perhaps that needs to be rephrased; it does look as if it's got enough vagueness that you're not really seeing the point. I have one specific reference in mind; I'll dig it out of the library soon. Michael Hardy 20:10, 8 September 2006 (UTC)
I indeed fail to see any point there. As for "common all over the place": no, mathematicians do not learn Aristotle's list. The uses of syllogisms I mentioned are not intentional, and are not marked explicitly as being syllogisms. Which is fine, because that's exactly the same situation as with the Hilbert's 10th problem. It would be more meaningful to consider only explicit uses of syllogisms, but under such interpretation the observation in the article makes even less sense. -- EJ 20:47, 8 September 2006 (UTC)

[edit] Doing something about the ridiculous date autoformatting/linking mess

Dear Glenford—you may be interested in putting your name to, or at least commenting on this new push to get the developers to create a parallel syntax that separates autoformatting and linking functions. IMV, it would go a long way towards fixing the untidy blueing of trivial chronological items, and would probably calm the nastiness between the anti- and pro-linking factions in the project. The proposal is to retain the existing function, to reduce the risk of objection from pro-linkers.Tony 14:57, 9 December 2006 (UTC)

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