Re: 1 equals 3 (among others)

*To*: mathgroup at smc.vnet.net*Subject*: [mg32188] Re: 1 equals 3 (among others)*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sat, 5 Jan 2002 00:10:24 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <a13v7l$dgb$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, > 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. huuuu, since when is (4 + Abs[x - 2] - x)/2 always 1 ? for all x A new finding at the TU Berlin ? Sqrt[a^2] is Abs[a] and *not* a ! > 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 knows it better. > > It took me hours to find this error in my rather complex setting...;-( hopfully is was your last error. But you don't report *all* of *your* errors to the mathgroup. Regards Jens