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FixedPoint stops "when elements no longer change"?

• To: mathgroup at smc.vnet.net
• Subject: [mg62776] FixedPoint stops "when elements no longer change"?
• From: "Steven T. Hatton" <hattons at globalsymmetry.com>
• Date: Mon, 5 Dec 2005 03:37:26 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

This is the example in The Mathematica Book for FixedPointList:

FixedPointList[Cos, 1.0]

{1., 0.540302, 0.857553, 0.65429, 0.79348, 0.701369, 0.76396, 0.722102, \
0.750418, 0.731404, 0.744237, 0.735605, 0.741425, 0.737507, 0.740147, \
0.738369, 0.739567, 0.73876, 0.739304, 0.738938, 0.739184, 0.739018,
0.73913, \
0.739055, 0.739106, 0.739071, 0.739094, 0.739079, 0.739089, 0.739082, \
0.739087, 0.739084, 0.739086, 0.739085, 0.739086, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085}

A bit of poking around showed me that this is using SameQ for SameTest.

"SameQ requires exact correspondence between expressions, except that it
considers Real numbers equal if their difference is less than the
uncertainty of either of them."

I guess I'm not seeing all the decimal places used to generate to list
above.  How would I determine the precision used to determine two
successive values are unchanged?

I tried FixedPointList[N[Cos[#], 2] &, 1.0], but that changed neither the
display, nor the result. 
-- 
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