The Definition Of 'Almost Surely' Is A Mathematical Nightmare

对"几乎必然"的定义是数学上的一个噩梦

If we were to say that a given event was almost sure to happen, how would you explain that to a small child? Maybe you'd say that the event was practically guaranteed, but then you'd have to explain what "practically" meant in regards to that sentence, which would just confuse things further. It's a tough question because the concept of something being "almost sure" to happen is so vague in and of itself.大学英语四级试题

如果我们说一个给定事件几乎必然要发生，你会如何向一个小孩子解释?也许你会说这件事几乎已经确定要发生，但稍后你还得解释在这句话中"几乎"是什么意思，而这会使事情更难理解。这是一个很难回答的问题，因为某件事"几乎必然"要发生的概念本身就是含糊不清的。

Luckily for us all, the concept exists within statistical mathematics, which explains it fully. Unluckily, it's incredibly intimidating at first glance. To quote an online math textbook on the concept:

对我们来说幸运地是，这一概念存在于统计数学中，统计数学充分地解释了这一概念。可不幸地是，统计数学对这一概念的定义乍一看却极度让人生畏。引用一本在线数学教科书对此概念的定义：

"In probability theory, a property is said to hold almost surely if it holds for all sample points, except possibly for some sample points forming a subset of a zero-probability event."

"在概率论中，如果除去一些可能构成一个零概率事件子集的样本点，其他的样本点都具有某种特性，那么我们就说这种特性是'几乎必然'存在的。"

In more basic language, that essentially means that even when an event has a 100 percent chance of occurring, it won't necessarily occur. For example, if you flipped a coin a million times, statistically, the odds of the coin landing on heads at least once is essentially one. However, there is an infinitesimally small chance that the coin could land on tails every single time. So although the odds of the event happening are for all intents and purposes guaranteed, it is impossible to say that.

更通俗地来说，上述定义本质上意味着即使一个事件发生的几率为百分之百，它也不一定就会发生。比如，你将一个硬币抛一百万次，从统计学上来说，硬币落下时至少有一次是正面朝上的概率基本上是1。然而，每次抛硬币时都存在极小的概率-硬币落下时是反面朝上的。因而即使确定一个事件发生的概率为百分之百，也不可能说它就一定会发生。

(责任编辑：田学江)