Talk:Growth of sequences

What now?

Is there any good way to encode this information for sequences? Half-baked thoughts:

• Use the index. Con: hard to keep in synch, huge list, clutters index, not feasible to search
• Use a dedicated page or pages on the wiki. Con: can't see from entry, not feasible to search.
• Wiki-style categories. Pro: arbitrary nesting. Con: hard to implement.
• New keywords. Con: many keywords needed, clutters keywords.
• New field parallel to keywords. Con: a pain to implement, many terms needed.

Cons shared by all these approaches:

• None of these allow the natural partial orders to show through, which would be very nice (and allows expansion, e.g. splitting a category in half).
• None of these conveniently allow sequences with lower bounds different from upper bounds.
• None allow more information where that is known.

To overcome these difficulties, a specialized field would be needed. For example:

0: [1, 0, -1; 0.5]

might mean $(n)^{1}(\log n)^{0}(\log \log n)^{-1}\cdot 0.5$ with the initial 0 meaning "take exp this number of times (or log if negative)". Two such fields, giving upper and lower bounds, would allow two-sided searches. But this has problems of its own: not only is it hard to implement and populate, but it's not clear how a user can enter searches (what would be intuitive?). So this isn't obviously better than other approaches.

I would be interested in new suggestions, improvements on existing ones, additional pros and cons, or preferences for or against any of these.

Charles R Greathouse IV 19:16, 26 January 2012 (UTC)

Maximilian Hasler likes the idea of categories, and gives specific suggestions here: User talk:M. F. Hasler/Categories. Charles R Greathouse IV 19:36, 26 January 2012 (UTC)