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Re: Mathematica bugs?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg67326] Re: Mathematica bugs?
*From*: Bill Rowe <readnewsciv at earthlink.net>
*Date*: Sun, 18 Jun 2006 05:13:23 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
On 6/17/06 at 4:36 AM, yaroslavvb at gmail.com (Yaroslav Bulatov) wrote:
>When I run the following line x = Pi/4; For[i = 0, i < 56, i += 1, x
>= 2*Abs[x - 1/2]]; N[x] I get 3.
>But x should always stay between 0 and 1, why do I get 3?
>Also x = Pi/4; For[i = 0, i < 50, i += 1, x = 2*Abs[x - 1/2]];
>N[Log[x]] gives me Indeterminate
>How can I get an indeterminate here?
The answer to both questions is loss of precision.
Note,
In[14]:=
x=Pi/4;For[i=0,i<56,i+=1,x=2*Abs[x-1/2]]
In[15]:=
x//FullSimplify
Out[15]=
56593902016227523-18014398509481984 Ï?
That is x is the difference between two large numbers.
In[16]:=
N[x,20]
Out[16]=
0.79387245267980382900
In[17]:=
%%//N
Out[17]=
0.
And finally the same computation is done more efficiently as
Nest[2 Abs[x-1/2]&, Pi/4, 55]//FullSimplify
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