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Re: it isn't strange?!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116167] Re: it isn't strange?!
  • From: Vincent <sheeplane at gmail.com>
  • Date: Thu, 3 Feb 2011 05:35:35 -0500 (EST)
  • References: <iibds7$nnd$1@smc.vnet.net>

On 2 Feb., 12:06, olfa <olfa.mra... at yahoo.fr> wrote:
> Hi Mathematica community,
>
> here is my pb:
>
>  input:
> Reduce[Max[a, b] == Max[c, d], c, Reals]
> output:
>  (d < Max[a, b] && c == Max[a, b]) || (d == Max[a, b] &&  c <= Max[a,
> b])
>
> when testing this output with 2 initialisations:
> d = 2  a =  4  b = 3  c = 6  here d < Max[4, 3] but c i=
s not equal to
> Max[4, 3]
>
> d = 4  a =   4  b = 3  c = 6  here d = Max[4, 3] but =
c is not <= to
> Max[4, 3]
>
> where is the pb?!


You are asking Mathematica to reduce the relation Max[a,b]==Max[c,d]
which it does correctly.
You then wonder why the numbers a=4,b=3 (Which gives Max[4,3]=4) and
c=6,d=2 (which have Max[6,2]=6) don't follow the result.

Well 4!=6. That is, for your chosen a,b,c,d it is not true that
Max[a,b]=Max[c,d]. So the numbers you "test" with don't follow the
inequality, so naturally the reduction doesn't either.

If you want to test the reduced relations you have to chose a set of
number for which relation actually holds. That means that the largest
number of a and b has to be equal to the largest number in c,d.


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