Re: Irrational numbers questions

David C. Ullrich wrote:

On Wed, 03 Jan 2007 12:57:34 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Does it follow now that sum(k=1..N)(1/k) - ln(N) is irrational?

Yes, because a rational plus an irrational is irrational.

Note: this is an approximation of the Euler-Mascheroni constant.

Right! Thus _all_ such approximations to the Euler-Mascheroni constant
gamma = lim(N->oo) sum(k=1..N)(1/k) - ln(N) are irrational. I can not
understand then how it would ever be possible that gamma itself can be
rational. I mean: isn't this already sufficient evidence that gamma is
not rational, hence irrational? Why not? Counter example of some such?

Han de Bruijn

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