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Checklists for establishing properties of objects

Checklists for establishing properties of objects

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. It is not easy use that fact to establish convergence, but you can use it to easily show divergence by picking out a divergent subsequence or two subsequences that converge to different limits." It was all rather straightforward and I didn't think it warranted a tricki article. In general, though, I think it would be useful to compile lists of results that would be useful in establishing that some object O satisfies property P, for standard types of P, and examples of what usually won't work and why. This kind of page would have a lot in common with pages in the "How to use X" category, and with tips on solving a particular class of problems pages, but maybe something more. I would appreciate it if everyone would share their thoughts on the relevance or irrelevance of this kind of article. What kind of properties can be easily established by going through a handy checklist?

This sounds like a good type of article, and starting with the sequence/limit example doesn't sound unreasonable. (There are other articles at this basic level.) Also, writing one type of article of this type may inspire others to
write similar ones.

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