Re: Irrational numbers questions

In article <98ae1$459bcb59$82a1e228$10981@xxxxxxxxxxxxxxxx> Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:
*** T. Winter wrote:

In article <740c3$459bbfc0$82a1e228$5308@xxxxxxxxxxxxxxxx>
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:
...
> 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?

lim{n -> oo} (1 - sqrt(1/n)) = 1.

Okay. And then lim{n -> oo} (a - sqrt(1/n)) = a for each rational a .
But somehow this is quite different from:

gamma = lim(N->oo) sum(k=1..N)(1/k) - ln(N)

where two _diverging_ quantities are substracted. Not that it's a good
argument that gamma should be irrational. Not yet.

This one?
lim{n -> oo} ln(e^2.(x + 1)) - ln(x)?
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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