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1 equals 3 (among others)


Dear group

Can anyone explain to me what is going on here? Look at this:

In[1]:=f[x_] = (4 - x + Sqrt[-4*(3 - x) + (x - 4)^2])/2;
In[2]:=Simplify[-4*(3 - x) + (x - 4)^2]
Out[2]=(-2 + x)^2

Well, right now we can be pretty sure that f[x]=1 for all x. But 
Mathematica (4.0.2.0X) seems to know better:

In[3]:=Map[f[#1]&, {0, 0.1, 1.7, 2, 2.5, 3}]
Out[3]={3, 2.9, 1.3, 1, 1., 1}

It took me hours to find this error in my rather complex setting...;-(

Bye, Grischa
-- 
-------------------------------------------------------------------------
   Grischa Stegemann                     Technische Universität Berlin --



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