O标记，O(∞)= O(1)? [英] O-notation, O(∞) = O(1)?

问题描述

一个快速的想法；有人可以说O(∞)实际上是O(1)吗?

So a quick thought; Could one argue that O(∞) is actually O(1)?

• 我的意思是，这不取决于输入的大小吗?
• 所以从某种角度来说，它是恒定的，即使它是无限的.

还是表达O(∞)的唯一正确"方法?

Or is the only 'correct' way to express it O(∞)?

推荐答案

无穷大不是数字，或者至少不是

Infinity is not a number, or at least not a real number, so the expression is malformed. The correct way to express this is to simply state that a program doesn't terminate. Note: program, not algorithm, as an algorithm is guaranteed to terminate.

((如果需要，您可以在超限定数上定义big-O表示法.不过，我不确定这是否有用).

(If you wanted, you might be able to define big-O notation on transfinite numbers. I'm not sure if that would be of any use, though.)

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