In article <3D937770.2863EBC7@gmx.de>,
 Christoph Hormann <chr### [at] gmxde> wrote:

> I'm not sure about the precise english terms, but math distinguishes
> between natural numbers (integers: 1, 2, 3, ...), rational numbers
> (numbers that can be represented as a fraction of two natual numbers) and
> real numbers (rational numbers and all other numbers like sqrt(2), pi,
> etc.).  The latter two categories are those where two consecutive random
> numbers from a given range won't be identical

If you can consider any two real numbers to be equal, it is possible for 
two consecutive random real numbers to be equal (if you could find a 
source of random reals...even analog circuitry would have a discrete 
number of steps). Rationals can even be represented with a computer, 
though you are practically limited by processing time and memory.

It *is* unlikely to happen in a finite range, and less likely the 
smaller the range. In an infinite random stream of numbers, *every* 
possible combination will occur, and the pattern of two consecutive 
equal real numbers is no less likely than any other pattern of two real 
numbers. 10 consecutive numbers being equal is no less likely than any 
other specific sequence of 10 numbers.

There is definitely no reason for it to be impossible...if you forbade 
these "runs", you wouldn't have a truely random sequence any more.


> (assuming there is a mathematical definition of random numbers in 
> that category, which i doubt).

Why not?

-- 
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/

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