Yes, π is computable. There are a few equivalent definitions of computable, but the most useful one here is the one you have given above: a real number r is computable if there exists an algorithm to find its nth digit. Here is such an algorithm.
Your last argument is not sound; you have confused the definition "can find the nth digit" with "can enumerate all the digits". The latter is not a useful definition: it rules out all the irrationals and many rationals as well!
An interesting fact is that the computable numbers are in fact countable, since we may Godel-number the Turing machines which produce them. Hence almost no reals are computable.
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是的，
π是可计算的。可计算有一些等效的定义，但这里最有用的一个是您上面给出的定义：如果存在一种算法来找到实数r，则它是可计算的nn第 位数字。 这里就是这样一个算法。你最后的论点并不合理；您混淆了“可以找到第 n 位数字”和“可以枚举所有数字”的定义。后者不是一个有用的定义：它排除了所有非理性和许多有理！
一个有趣的事实是，可计算的数字实际上是可数的，因为我们可以对产生它们的图灵机进行哥德尔编号。因此几乎没有实数是可计算的。
Yes,
πis computable. There are a few equivalent definitions of computable, but the most useful one here is the one you have given above: a real numberris computable if there exists an algorithm to find itsnth digit. Here is such an algorithm.Your last argument is not sound; you have confused the definition "can find the
nth digit" with "can enumerate all the digits". The latter is not a useful definition: it rules out all the irrationals and many rationals as well!An interesting fact is that the computable numbers are in fact countable, since we may Godel-number the Turing machines which produce them. Hence almost no reals are computable.