Re: 1 equals 3 (among others)

*To*: mathgroup at smc.vnet.net*Subject*: [mg32195] Re: [mg32180] 1 equals 3 (among others)*From*: BobHanlon at aol.com*Date*: Sat, 5 Jan 2002 00:10:34 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 1/4/02 6:07:44 AM, Stegemann at physikDONOT.SPAMtu-berlin.de writes: >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...;-( > Sqrt returns a positive number Simplify[Sqrt[(x-2)^2], x>=2] -2 + x Simplify[Sqrt[(x-2)^2], x<2] 2 - x Plot[{Sqrt[(x-2)^2]}, {x, 0, 5}]; Bob Hanlon Chantilly, VA USA