I read the Volokh Conspiracy daily and with the possible exception of How Appealing its my favorite weblog.

Yesterday some math came up and so and I wanted to chip in on the orderings posting.

Technically speaking, it is not well-defined to speak of whether a "set" is ordered. You need to be looking at a set S together with some relation, denote it <. Thus your example of pairs of real numbers not being ordered is not strictly correct. What you mean is that pairs of real numbers with < defined to mean (a,b) < (c,d) exactly when a < c and b < d is not strict ordering. However, one can perfectly well choose an ordering of the set of pairs of real numbers by say (a,b) < (c,d) if a < c or if a=c and b < d. This is called "lexicographic ordering" and is often very convenient.

An example where this is more interesting is say the positive integers where one can give a partial ordering by < and another one by a << b when b is a multiple of a. Both of these are very important partial orderings on the positive integers, but only one is a strict ordering.

Anyway, they're all rather trivial points, but the blogosphere functions by having people nitpick where they happen to be knowledgable.

Incidentally Sasha is a law/ec student at Harvard (like ben) and I walk by his appartment almost daily.