User talk:Gro-Tsen

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Hi there! On the kind of point you're raising about algebraic geometry pages - it seems fair to say that we are short of experts on all the main divisions of pure mathematics for the last half-century. That is, getting past 1950 or so is always quite tough, given that the basics have to be built up from scratch. So please don't feel inhibited about adding material. As they say, be bold!

The one point I would make is that it is all incremental. There is no real answer to the question 'how many types of scheme need a mention?' Maybe if the abelian variety coverage were built up, it would be one thing; if we started to have some singularity theory, or moduli space articles, or more coherent cohomology discussed, other things. I'm sure you get the point - in the end it should add up to something much more integrated, but it works out that additions are always piecemeal.

Charles Matthews 22:00, 16 Feb 2004 (UTC)

Don't bother with the translation French-English, just write the French page, and I'll translate (Tu pourrais aussi faire l'inverse, mais je ne sais pas si t'as confiance dans mon français). Schopenhauer 18:40, 17 Feb 2004 (UTC)

[edit] On ordinal numbers

To Gro-Tsen: Regarding your changes to the ordinal number page on March 6, 2006. 1. "so-called" seems to denigrate "well-order", which I feel is inappropriate. 2. I cannot imagine that a good mathematician would confuse ordinals with well-orderings of other sets. 3. Using "" leaves omega in an italicized form which is inconsistent with the rest of the article where the ordinary form of omega is used for the least infinite ordinal. 4. Why make a temporary definition? Just say that the (real) definition is below. 5. "lexicographically" is a good edit. -- JRSpriggs on March 6, 2006

(1) The reason for the "so-called" is to make it clear that the intro (but only the intro) of the ordinal number article ought to be understandable by a reader who does not know what a well-ordered set is. So what I mean to say is "a certain structure which is called well-ordered sets, for which we refer to another article but which the reader need not know about for the moment". I don't think "so-called" is derogatory, and I can't find a better way of conveying the meaning I intend to convey (but if you can think of such a way, do state it).

(2) I consider myself a mathematician: I don't know about "good", but I don't think I'm suggesting this confusion out of incompetence. Seriously, the point is that while it makes sense to distinguish isomorphic objects when the isomorphism is not canonical (e.g., to speak of an algebraic closure of a field, rather than the algebraic closure), in the category of well-ordered sets all isomorphisms are unique, so the distinction between two isomorphic well-ordered sets can be considered hair-splitting. (Of course, when the well-ordered sets have some extra structure such as being subsets of some larger set or something of the sort, then the distinction needs to be made. But my point is that just as one tends to disregard the distinction between Z/2Z and any "other" group with two elements it is a reasonable abuse of language to consider any well-ordered set of type ω to be ω. Naturally, we aren't really "confusing" the sets, we just let canonical isomorphisms left unstated. Such a point of view is common in category theory, and set theorists of course do not have a monopoly on ordinal numbers.) But, more to the point, from the pedagogical point of view I think the remark is worth making, because I've already noticed that some beginners manage to grasp one of the concepts of "ordinal" and "well-ordered set" without understanding the other, which is strange: so this note is supposed to help them realize that they should transfer their understanding from one to the other. Again, if you feel strongly, try to suggest a way to rephrase this. But remember the intro is supposed to be mostly pedagogical (more than the rest of the article, at least).

(3) We should check in the manual of style, but I'm pretty sure we're not supposed to mix HTML markup with LaTeX-style markup. Remember that LaTeX-style might be rendered as MathML (using BlahTeX or whatever) and I don't think it likes this sort of mix. If you write ω·<math>\gamma</math>, someone set preferences to display even simple equations using PNG images will see the gamma as an image and the omega as text, which is worse than the problem you describe, I think. Now maybe we <math> should have been used all the way along, I don't know.

(4) Well, I don't care much about that one, really, so you can change it back if you really care. I just wanted to make the point that, for many purposes, one doesn't need to know what ordinal multiplication is in general, merely left-multiplying by ω is enough, and it just amounts to indexing the limit ordinals.

--Gro-Tsen 11:43, 7 March 2006 (UTC)

OK. I let you have 2,3,4. And I will try to reword 1 ("so-called"). JRSpriggs 10:10, 8 March 2006 (UTC)

I just read the Wikipedia article on Cofinality; and it supports my version of cofinality as including 1 as the cofinality of a ordered set with a greatest element in the set. So I am tempted to remove the qualification from the revised subsection on cofinality. Do you agree? JRSpriggs 07:13, 10 March 2006 (UTC)

Tell you what. I will just take out the qualifications. If you disagree, you can revert it to the version I created yesterday. JRSpriggs 09:38, 10 March 2006 (UTC)

I like your additions to "cofinality". JRSpriggs 10:32, 12 March 2006 (UTC)

[edit] Oppose plan to move "Ordinal number"!

Some people are planning to move the article Ordinal number. Since you were once very active in editing this article, I would hope that you would express your opposition to this disasterous idea at Talk:Ordinal number#Should the article really be called transfinite ordinal numbers. JRSpriggs 07:30, 8 September 2006 (UTC)

To be honest, I don't care very much. That is to say, I very mildly agree with you that the article shouldn't be renamed, but not enough to enter the "tempest in a teapot". If it comes to a vote, I'll cast a weak one, but so long as it's just a debate, I'll leave it at that. It's a shame, though, how much time can be wasted by people who want the naming of the articles to be absolutely perfect, when that time could be spent by actually writing useful articles. --Gro-Tsen 08:59, 9 September 2006 (UTC)