On 13/02/2013 01:43, Keith F. Lynch wrote:

Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:

...

Surely that proves only that there are *some* N such that the average over the first N years is log 2.

I don't understand what you mean. Since every year's length is a whole number of days, the average length of years 1 through N will always be a rational number, hence will never be the natural log of 2. (Though it will get closer and closer as N grows larger.)

Sorry, I was sloppy and unclear. I meant: it proves only that there are *some* N forming a subsequence along which the average tends to log 2. The point is that that property is compatible with there being other N for which the average is far from log 2, so (unless the N!-based argument somehow proves more than it seems to) more is needed to prove that the average actually -> log 2 over the whole sequence, rather than just over some subsequence. -- g