Re: Irrational numbers questions

In article <1168464314.257076.263370@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> Han.deBruijn@xxxxxxxxxxxxxx writes:
....
You've just contradicted yourself: if it's less than the maximum, it's
certainly not between RS(L) and RS(U). And you still haven't
_defined_ it for irrational numbers.

That's true. But what I want is the maximal simplicity for real numbers
which are suspect to be irrational. The example I am working on is the
Euler-Mascheroni constant. But meanwhile I've defined the simplicities
of (all, known) irrational numbers as being exactly zero.

With you program you can prove nothing. But try an easier example first
with your method: sqrt(2).

The RS functions cannot distingush between different
irrational numbers, because they are all zero for them. But again, our
simplicities are supposed to be useful for reals which are _not known_
yet as to be irrational or not.

Show us first a number where it works better than a standard irrationality
proof.

They are meant as a sort of continuous
transition between rationality and irrationality. I mean, perhaps gamma
is not rational and not irrational and such an in-between number. Or am
I saying something stupid now?

Yes. As the defition of irrational numbers is "a number that is not
rational", that is indeed stupid.
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