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MathGroup Archive 2004

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Re: functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45525] Re: [mg45481] functions
  • From: Selwyn Hollis <sh2.7183 at misspelled.erthlink.net>
  • Date: Mon, 12 Jan 2004 02:15:35 -0500 (EST)
  • References: <200401100500.AAA02409@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

This is a pretty wild idea, but how about the following as a criterion 
for deeming a single-precision floating-point number between 0 and 1 to 
be "irrational": It's irrational if its base-10 form contains all 10 
digits, more precisely, if

   IrrationalQ[x_] := Length[Union[IntegerDigits[Round[10^16*x]]]] == 10

returns True. Then

   grph = Plot[If[IrrationalQ[x], x, 0], {x, 0, 1}, PlotPoints -> 100]

draws a graph that, with a little imagination, suggests what the graph 
of
If[x is irrational, x, 0] could look like.

Still better is

   Show[Graphics[{AbsolutePointSize[1.5], Point[#]} & /@
          (grph/.Graphics[{{Line[z_]}}, ___] -> z)]]

This is all nonsense, of course, but fun nonetheless.

Experiments show that IrrationalQ[Random[]] returns True with 
probability roughly 0.07. (Anybody have a clue why?)

-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis
(edit reply-to to reply)

On Jan 10, 2004, at 12:00 AM, lorenzo.keegan at handbag.com wrote:

> Hello,
>
> Can you help me?
>
> How do write expressions in Mathematica for functions and sequences
> such as the following:
>
>       f(x) = {1/x,  x is irrational
>              {x^2,  x rational
> and
>
>       f(n) = 1/n, n odd
>              n^2, n even
>
> I am a new user and find the manual rather daunting.
>
> Best wishes
> Laurence Keegan
>
>
>
>
>


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