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MathGroup Archive 2005

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FindInstance question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55736] FindInstance question
  • From: János <janos.lobb at yale.edu>
  • Date: Tue, 5 Apr 2005 03:20:55 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

If I am looking for the solution set of x < x^2, Reduce gives me the  
answer:

In[14]:=
Reduce[x < x^2, x]
Out[14]=
x < 0 || x > 1

I tried to use FindInstance and ListPlot to visualize it for my 7th  
grade son, based upon the example on the Book Section 3.4.8.

In[15]:=
FindInstance[x < x^2, x,
   Reals, 50]
Out[15]=
{{x -> -4375}, {x -> -4304},
   {x -> -4089}, {x -> -3945},
   {x -> -3707}, {x -> -3682},
   {x -> -3486}, {x -> -3414},
   {x -> -3331}, {x -> -3286},
   {x -> -3248}, {x -> -3018},
   {x -> -2974}, {x -> -2953},
   {x -> -2941}, {x -> -2877},
   {x -> -2864}, {x -> -2687},
   {x -> -2525}, {x -> -2373},
   {x -> -2108}, {x -> -2074},
   {x -> -1773}, {x -> -1403},
   {x -> -1402}, {x -> -1348},
   {x -> -1092}, {x -> -566},
   {x -> -51}, {x -> 77},
   {x -> 195}, {x -> 1181},
   {x -> 1216}, {x -> 1547},
   {x -> 1687}, {x -> 1765},
   {x -> 1876}, {x -> 2040},
   {x -> 2713}, {x -> 2734},
   {x -> 3018}, {x -> 3312},
   {x -> 3455}, {x -> 3503},
   {x -> 3704}, {x -> 3927},
   {x -> 3974}, {x -> 3985},
   {x -> 4349}, {x -> 4944}}

Well, the closest values to 0 and 1 are -51 and 77.  It is not  
terrible useful to ListPlot them.  If I select 500 points instead of  
50 it just gets worse.

My question is:

1,  Is it possible to suggest FindInstance to use values "much  
closer" to the boundaries of 0 and 1 or

2 If it is not possible, what methods others would use for this  
situation to visualize ?

I tried

In[18]:=
FindInstance[x < x^2 &&
    x > -2 && x < 2, x, Reals,
   50]

but that is not the original inequality :)
I also tried to replace the Reals domain with something - logical  
looking - else, but Mathematica really wants a built in domain there.

In[32]:=
FindInstance[x < x^2, x,
   x > -2 && x < 2, 50]

or

In[37]:=
FindInstance[x < x^2, x,
   {-2, 2}, 50]

and it complained:

FindInstance::"bddom":"Value \!\(\(\(x > \(\(-2\)\)\)\) && \(\(x < 2\) 
\)\) of \
the domain argument should be Complexes, Reals, Algebraics, Rationals, \
Integers, Primes, Booleans, or Automatic. \
\!\(\*ButtonBox[\"More\[Ellipsis]\", ButtonStyle->\"RefGuideLinkText 
\", \
ButtonFrame->None, ButtonData:>\"FindInstance::bddom\"]\)"


A  non existent "user defined Domain" would be handy here.  I am  
thinking of a

myDomain[x_Real]:=UserDefinedDomain[x > -2 && x < 3]

or similar construction to put into FindInstance.  Is that too much  
to ask ?

Thanks ahead,

János




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