什么是定点? [英] What is fixed point?

问题描述

我正在重新观看有关 SICP 的一些早期讲座.定点的概念让我有些困惑.定点过程:我应该这样考虑吗，这是找到给定函数的定点的方法."那么给定f(2) = 2呢?

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?

为什么在此讲座中，那么映射到x / y的新功能y是一个固定点吗?

Also why is it stated in this lecture, that a new function y that maps to x / y is a fixed point?

推荐答案

正义者的答案解决了一个固定点，但这仍然留下您问题的另一部分:

Just Ethier's answer addresses what a fixed point is, but this still leaves the other part of your question:

为什么新函数y映射到x/y是一个固定点?

Also why is a new function y that maps to x / y a fixed point?

讲师在您提到的那一点上讲得很快，但是我认为他实际上是在说√ x是多个函数的固定点，而显然√ x是固定点是

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

    y ↦ x / y

因为

   √ x = x/√ x

    √x = x / √x

但是，给定的用于计算固定点的过程不适用于该函数，因为其内部过程iter会在初始值上循环，并将该函数应用于初始值.因此，新值/旧值的顺序为(1,2)，(2,1)，(1,2)，...

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), …

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