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Monday, November 19 2012

Exercises in Set Theory and Teen Reminiscences

I recently spent some time to solve some exercises from Thomas Jech's book "Set Theory" and to typeset my solutions. I'm now done with the six first chapters, that is half of the first part of the book... entitled "Basic Set Theory". Well, I'll probably have to finish the second half to be able to claim that it is "basic" and then I'll still have a lot to study in the two other more advanced parts ;-) New exercises are essentially for chapter 4, as I was already almost done with the other chapters before. That was good to do some topology again! (without using the axiom of choice!)

It was also funny to solve exercise 5.4: if a set A can be well-ordered then P(A) can be totally ordered. It recalls me when I was 13-14 and was trying to well-order sets constructed from other well-ordered sets. Of course (*), I was stuck on how to build a well-ordering on the powerset of a well-ordered set but I had however been able to construct the linear order described in exercise 5.4. Nowadays, my old proof looks overcomplicated although it could probably be simplified if one uses the symmetric difference and relies on well-known set properties. My most recent proof is much simpler but still not really straightforward as I do not see other ways than testing each case. If someone has a better solution, please post a suggestion...

Here are the links to each chapter:

(*) Some years later, someone congratulated me by email for my wonderful proof of how to well-order P(A) from a well-ordering on A. However, my proof had never been finished and will remain uncomplete. If we can prove in ZF that for any well-orderable set A, its powerset P(A) is well-orderable then it is easy to prove by ordinal induction that all V α's are well-orderable and thus the theorem of Zermelo, which is equivalent to the axiom of choice. But this one is well known to be independent from the other axioms of ZF...

Saturday, November 27 2010

Ingénieur en informatique / Computer Engineer

J'ai le plaisir d'annoncer que je suis maintenant officiellement ingénieur ENSIIE :-) J'ai aussi mis mon CV en ligne...

I'm pleased to announce that I'm now officially an ENSIIE engineer :-) I've also uploaded my CV/resume...

Tuesday, September 7 2010

Farvel Danmark, Bonjour Paris.

Så bliver det tre uger siden jeg forlod Århus. Jeg vil gerne take alle for et hyggeligt ophold og jeg håber at vi mødes igen! Jeg regner også med at blive en datalogiingeniør snart. De to næste år, skal jeg læse matematik ved Paris' Universitet. Så hvis i kommer til fransk hovedstad, i er meget velkommen til at besøge mig ;-)

Après une année Erasmus, j'ai finalement terminé ma formation d'ingénieur ENSIIE et espère obtenir mon diplôme bientôt ! Je suis maintenant de retour sur Paris et compte poursuivre ma formation en mathématiques à l'Université Pierre et Marie Curie (Paris VI). Au premier semestre mon choix se porte sur les modules de théorie de Galois et d'analyse réelle. J'envisage aussi de commencer une nouvelle langue parmi allemand, russe ou chinois... affaire à suivre !

Sunday, May 2 2010

Mise en place d'un blog

Voilà, je viens de mettre en place ce blog aujourd'hui. J'espère ainsi profiter des avantages offerts par ce medium: syndication de contenu, archivage en catégories, possibilité d'avoir des commentaires etc. Je compte m'en servir pour parler de mes différents travaux et il me sera alors indispensable de pouvoir utiliser le format XHTML+MathML+SVG. Par conséquent, mon prochain billet sera sur la manière de paramètrer Dotclear pour pouvoir répondre à ce besoin.