FixedPoint is a procedural rather than mathematical function. This is quite clear from the documentation by the way, so that should have been the first place to check. As for the mathematical way to determine the exact value, Solve can be used for that.
FixedPoint
Solve
Thanks for your reply. I know now. Have a nice day!
Eric, that is a very good explanation.
One could wish that the WL documentation had more of this nuts and bolts approach.
Hi Zhenyu
When you provide exact numerical input WL evaluates exact output. Compare
NestList[(# + 2/#)/2 &, 1, 6]
and
NestList[(# + 2/#)/2 &, 1., 6]
The first one will never terminate.
Hi Rohit,
May you tell me what's the WL evaluates
And may you tell me why the first wouldn't terminate?
(1) A function that keeps changing after every application is not going to reach a fixed point. If the evaluations produce exact results then no tolerance specification will be used.
(2) You really need to read the documentation.
(3) Also check the documentation for RSolve. It is the function to try first for determining the exact limiting value.
RSolve
But why the second will reach a fixed point?
Check the documentation for SameQ, in particular the first item under Details and Options.
SameQ
