### Rough idea of unwritten article

Often it is easier to deal with objects that are roughly the same size. If the range of sizes isn't too great, then we can achieve this by picking a large subset of the objects we have at hand, or partitioning them into not too many sets. For example, if the integers all lie between and , we can partition them into at most sets such that any two in the same cell of the partition are within a factor of 2 of each other. This very simple trick is very useful, though it often comes at the expense of extra logarithmic factors in proofs.

It would definitely be good if someone could write this article, and even better if they can think of a good way of classifying the article—it is not altogether obvious how to do so, as the basic idea is used in many different contexts. But how would somebody who needed it stumble on it in the Tricki?

## Comments

## Dyadic pigeonhole principle

Thu, 16/04/2009 - 18:40 — taoI wrote something on this (the "dyadic pigeonhole principle") at

http://www.math.ucla.edu/~tao/preprints/Expository/pigeonhole.dvi

I may try to convert this to the wiki format, but probably not soon.