电脑中最大的数字是多少? [英] What's the biggest number in a computer?

问题描述

我5岁的孩子问:计算机中最大的数字是什么?

我们不是在讨论特定数据类型的最大数量，而是一台计算机可以代表的最大数量.

不允许无穷大.

更新我的孩子总是想打印为好吧，所以可以说计算机的需求打印这个号码和孩子知道这是一个很大的数目.当然，实际上，我们不会打印，因为没有足够的树木.

解决方案

这个问题实际上是一个非常有趣的问题，数学家对此进行了相当多的思考.您可以在这篇文章中进行阅读，这是一篇引人入胜的有趣文章.

简而言之，一个名叫Tibor Rado的家伙着手通过定义一个称为Busy Beaver数字的序列来查找一些非常大但仍定义明确的数字.他将BB( n )定义为在输入 n 个符号的情况下，图灵机停止前可以执行的最大步数.请注意，这个序列本质上不可计算，因此数字本身虽然定义明确，但很难确定.这是前几个:

  BB(1)= 1BB(2)= 6BB(3)= 21BB(4)= 107 

...等等...

  BB(5)> = 8,690,333,381,690,951 

没有人能确定BB(5)到底有多大，但这是有限的.而且没有人知道BB(6)及以上的体积有多大.但是，至少这些数字在数学上是完全定义明确的，与人类从未想过的最大数字加一个"不同.;)

那呢:

计算机可以代表的最大数量是程序足够小以适合其可用内存后在停止之前可以执行的最多指令.

平方.

不，等等，立方体.不，提高了自身的力量！

该死！

Just asked by my 5 year old kid: what is the biggest number in the computer?

We are not talking about max number for a specific data types, but the biggest number that a computer can represent.

Infinity is not allowed.

UPDATE my kid always wants to print as well, so lets say the computer needs to print this number and the kid to know that its a big number. Of course, in practice we won't print because theres not enough trees.

解决方案

This question is actually a very interesting one which mathematicians have devoted a fair bit of thought to. You can read about it in this article, which is a fascinating and accessible read.

Briefly, a guy named Tibor Rado set out to find some really big, but still well-defined, numbers by defining a sequence called the Busy Beaver numbers. He defined BB(n) to be the largest number of steps any Turing Machine could take before halting, given an input of n symbols. Note that this sequence is by its very nature not computable, so the numbers themselves, while well-defined, are very difficult to pin down. Here are the first few:

BB(1) = 1
BB(2) = 6
BB(3) = 21
BB(4) = 107

... wait for it ...

BB(5) >= 8,690,333,381,690,951

No one is sure how big exactly BB(5) is, but it is finite. And no one has any idea how big BB(6) and above are. But at least these numbers are completely well-defined mathematically, unlike "the largest number any human has ever thought of, plus one." ;)

So how about this:

The biggest number a computer can represent is the most instructions a program small enough to fit in its available memory can perform before halting.

Squared.

No, wait, cubed. No, raised to the power of itself!

Dammit!

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