Re: Bizarritudes

On Wed, 27 Jul 2005 14:40:29 +1000, Gerry Myerson
<gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

>Here is a hypothesis:
>
>Any number you get starting with integers and applying the operations
>x + y, x - y, xy, x / y, x^y, log(x) any finite number of times
>will either be rational or else every digit will occur infinitely
>often in its decimal expansion.

I would conjecture more: that every number generated is either
rational or normal.

But there's not much risk being taken here -- such a conjecture is an
almost sure thing since I think it's been shown that almost all real
numbers are normal, hence the likelihood of hitting a non-normal
irrational number with a specified countable sequence is 0. You'd have
to be incredibly unlucky to be wrong.

But then again, with my luck, since I'm now supporting the conjecture,
that could easily tilt the probability back the other way.

quasi
.

Relevant Pages
Quantcast