Re: 1 equals 3 (among others)

• To: mathgroup at smc.vnet.net
• Subject: [mg32187] Re: 1 equals 3 (among others)
• From: "Mikael Persson" <lillpele79 at hotmail.com>
• Date: Sat, 5 Jan 2002 00:10:23 -0500 (EST)
• References: <a13v7l\$dgb\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <a13v7l\$dgb\$1 at smc.vnet.net>, "Grischa Stegemann"
<Stegemann at physikdonot.spamtu-berlin.de> wrote:

> 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

When I calculated I got that

f(x) = 1 if x >= 2
and
f(x) = 3-x if x<2

Your mistake is that you claim that sqrt((x-2)^2)=x-2. But it is |x-2|

regards

Micke P

```

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