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Re: Creating a Random Function to Select an Irrational

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102210] Re: [mg102176] Creating a Random Function to Select an Irrational
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sat, 1 Aug 2009 04:01:33 -0400 (EDT)
  • References: <200907310957.FAA19545@smc.vnet.net>
  • Reply-to: drmajorbob at bigfoot.com

The good news is, 100% of real numbers are irrational. That is, the odds  
of selecting a real at random and getting a rational is precisely zero.

The bad news is, machine-precision (and arbitrary precision) real numbers  
are 100%, unanimously rational. So are their sums, differences, products,  
and ratios.

(The good and bad news may seem contradictory, but they are not.)

So, the only way to get irrational numbers in Mathematica is using symbols  
(Pi, E, for instance) and expressions you know are irrational, such as  
Sqrt[2]. Your link shows a few other ways. But it's hard to call creating  
one of these "random".

You could make a long list of irrational numbers and randomly sample them,  
perhaps adding several together... but I don't see what you could prove or  
accomplish, with such a procedure.

Bobby

On Fri, 31 Jul 2009 04:57:40 -0500, BenT <brtubb at pdmusic.org> wrote:

> Although Mathematica has built-in functiona to obtain random integers  
> and real
> numbers, I need to select a random irrational number. At this
> webpage,
>
> http://mathworld.wolfram.com/IrrationalNumber.html
>
> several definitions are given for known conditions to create
> irrational numbers, such as
>
> Numbers of the form n^(1/m) are irrational unless n is the mth power
> of an integer.
>
> Can anyone define a function to allow a similar capability as Random[]
> in selecting a "member" from the above defined "set" of values, or any
> other of the definitions listed on the same webpage?
>



-- 
DrMajorBob at bigfoot.com


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