Tricki - General discussion

Countable but impredicative

mmacdoug — Sat, 13 Nov 2010 09:38:17 +0000

I would be most interested to learn of examples of sets which are countable but impredicatively defined. For clarity, I should add that by 'countable', I mean that there exists a surjection from the natural numbers (or the natural numbers excluding zero) to the set.

I look forward to hearing from interested forum members.

Techniques for proving convergence

devin — Sat, 25 Apr 2009 07:21:25 +0000

How would you feel about having a ``Techniques for proving convergence'' entry in the What kind of problem am I trying to solve? page?

A different kind of article?

gowers — Thu, 23 Apr 2009 08:52:11 +0000

There are some proofs that keep getting mentioned on the Tricki. One example is the proof of Roth's theorem on arithmetic progressions, which is a very important argument for the Tricki because (i) it illustrates many different "tricks" and (ii) it can be thought of as a starting point for many more.

This situation is likely to recur again and again, and suggests the possibility of a rather nice kind of article.

Different levels in the same topic

jbd — Thu, 16 Apr 2009 15:31:32 +0000

I was reading over the article on "How to solve quadratic equations", which is fine as written if it's a teacher who needs to explain the topic and needs a refresher on all the different approaches, or a college undergraduate who hasn't taken that level of algebra for a while. But I would hesitate to send an actual neophyte to solving quadratic equations to the same page; it's written at too high a level. Might it be worth it to make "elementary" versions of some pages (with some appropriate logistics for naming attached), or are we presuming our audience won't be of that level?

Checklists for establishing properties of objects

sobal — Thu, 16 Apr 2009 13:45:26 +0000

The particular example I have in mind is establishing convergence or divergence of a sequence. I recently tutored a first course in real analysis where the students didn't know where to start with such questions. I wrote them a checklist of properties that would imply convergence and properties that would imply divergence, and also pointers like "If a sequence converges to a limit L, every subsequence converges to L.

Categorization

gowers — Thu, 16 Apr 2009 12:23:09 +0000

I would like to encourage people to think about how to categorize articles in such a way that they are likely to be found by those who need them. A good way of starting to think about this is to click on "Top level" (in grey at the top of any of the mathematical articles) and then on "Uncategorized" to see a list of currently uncategorized articles. How should they fit into the structure of the Tricki? Often there will be two answers, one based on subject matter and one on the kind of problem that a technique is useful for.