scheme - SICP - Which functions converge to fixed points? -

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in chapter 1 on fixed points, book says can find fixed points of functions using 

f(x) = f(f(x)) = f(f(f(x))) ....

what functions?

it doesn't work y = 2y when rewrite y = y/2 works

does y need smaller everytime? or there general attributes function has have find fixed points method?

what conditions should satisfy work?

according banach fixed-point theorem, such point exists iff mapping (function) contraction. means that, example, y=2x doesn't have fixed point , y = 0,999... * x has. in general, if f maps [a,b] [a,b], |f(x) - f(y)| should equal c * |x - y| 0 <= c < 1 (for x, y [a, b]).


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