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

**Follow-Ups**:**Re: FindInstance question***From:*DrBob <drbob@bigfoot.com>