Re: BigDecimal and trigonometrics

Googmeister wrote: 
Roedy Green wrote:

On Wed, 16 Nov 2005 16:56:02 GMT, Jeffrey Schwab
<jeff@xxxxxxxxxxxxxxxx> wrote, quoted or indirectly quoted someone who
said :


But can you please point me to an irrational number
that cannot be derived by a sequence of mathematical operations on
rational numbers?


The time until George Bush's death in microseconds from noon UTC
today.



Nice one. :)

Choose a random number uniformly between 0.0 and 1.0.
It will almost surely be uncomputable.

Nice job. I think you've actually got me there. :) We could certainly use symbols to stand for these numbers, but I don't think the symbols could really be said to "represent" the irrationals; for example, I don't think symbolic representations could be used to order such random numbers. Just for giggles, here's a way to assign symbols to truly random numbers:

In order to be observed, such numbers must be generated by some process, at some finite rate. (It is understood that other irrational numbers exist, but it should also be understood that only finite number may ever be observed by people or computers, since there is a finite number of people and computers, each having finite faculties of observation.) We can then refer to the first number generated by the process as R1, the second as R2, etc. Randoms generated at the same instant may be refered to as RnA, RnB, etc., where n is an ordinal integer.
.

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