I'm rewatching some of the earlier lectures on SICP. The notion of a fixed-point is a bit confusing to me. The fixed-point procedure: should I be thinking about it this way, "it's the way to find a fixed-point of a given function." So given f(2) = 2
?
Also why is it stated in this lecture, that a new function y
that maps to x / y
is a fixed point?
Just Ethier's answer addresses what a fixed point is, but this still leaves the other part of your question:
The lecturer is speaking quickly at the point that you mentioned, but I think that he's actually saying that √x is the fixed point of more than one function, and that an obvious function of which √x is a fixed point is
y ↦ x / y
since
√x = x / √x
However, the given procedure for calculating fixed points would not work for this function, because its internal procedure
iter
loops on an initial value and the function applied to the initial value. Thus the sequence of new/old values is (1,2), (2,1), (1,2), …