blocks|key|1578179|text|根据前两个定义，不应该存在交叉，因为总是这个词。|type|unstyled|depth|inlineStyleRanges|offset|length|style|BOLD|entityRanges|data|1578180|f(n)+=Ω(g(n))指的是f(n)上的下界，使得f(n)总是≥c.g(n)
f(n)+=+O(g(n))指c.g(n)是f(n)上的一个上界，使得f(n)总是≤c.g(n)|blockquote|1578181|这些定义不完全正确，。因为大O表示法的思想是在n真的很大的时候检查操作的数量。从外行的角度来说，这意味着只有在你认为足够大的某个数字之后，你才开始检查复杂性。在你的图片上概述了这一点：|CODE|1578182|上界和下界对n>+n0有效.|1578183|这就是为什么图片上有一条垂直线n0。所以，在这行之前，您不关心任何事情，因为您只考虑n0之后的数字足够大。|1578184|要使这些定义完全正确，只需将n>+n0添加到它们的末尾即可。|1578185|entityMap^0|I|2|0|0|0|A|N|1|0|0|0|0^^$0|@$1|2|3|4|5|6|7|T|8|@$9|U|A|V|B|C]]|D|@]|E|$]]|$1|F|3|G|5|H|7|W|8|@]|D|@]|E|$]]|$1|I|3|J|5|6|7|X|8|@$9|Y|A|Z|B|C]|$9|10|A|11|B|K]]|D|@]|E|$]]|$1|L|3|M|5|H|7|12|8|@]|D|@]|E|$]]|$1|N|3|O|5|6|7|13|8|@]|D|@]|E|$]]|$1|P|3|Q|5|6|7|14|8|@]|D|@]|E|$]]|$1|R|3|-4|5|6|7|15|8|@]|D|@]|E|$]]]|S|$]]

Based on the first two definitions, there should not be an intersection because of the word always

<blockquote>
 f(n) = Ω(g(n)) means c.g(n) is a lower bound on f(n) such that f(n) is
 always ≥ c.g(n)
 
 f(n) = O(g(n)) means c.g(n) is an upper bound on f(n) such that f(n)
 is always ≤ c.g(n)
</blockquote>

These definitions are not exactly correct. Because the idea for big-O notation is to check the number of operations when <code>n</code> is really big. In layman terms it means that you start checking the complexity only after some number which you consider big enough. This is outlined on your picture:

<blockquote>
 Upper and lower bounds valid for n > n0 ...
</blockquote>

and this is why on the picture you have a vertical line n0. So you do not care about anything before this line, because you consider only numbers after n0 big enough.

To make these definitions exactly correct, just add for n > n0 at the end of both of them.

blocks|key|2179377|text|这个定义根本是不准确的。大O表示法是关于渐近增长的.因此，它的性质被认为是“足够大的N"，这意味着它可能不适用于小N。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2179378|在图表中，“足够大的N”标记为N0，然后保持限制属性。|2179379|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|F|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|G|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|H|8|@]|9|@]|A|$]]]|E|$]]

The definition is simply inaccurate. Big-O notation is about asymptotic growth. As such, it's properties are considered for "large enough N", which means it might not hold true for small N's.

In the chart, a "large enough N" is marked as N0, after which the limiting property is maintained.

blocks|key|2179443|text|除了在其他答复中已经说过的话外，定义中的不平等也是不正确的，应予以扭转：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2179444|f(n)+=Ω(g(n))指的是f(n)上的下界，使得f(n)总是≥c.g(n)
f(n)+=+O(g(n))指c.g(n)是f(n)上的一个上界，使得f(n)总是≤c.g(n)|blockquote|2179445|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|G|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|H|8|@]|9|@]|A|$]]|$1|E|3|-4|5|6|7|I|8|@]|9|@]|A|$]]]|F|$]]

In addition to what has been already said in other answers, the inequalities in the definition are incorrect as well, they should be reversed:
<blockquote>
f(n) = Ω(g(n)) means c.g(n) is a lower bound on f(n) such that f(n) is always ≥ c.g(n)
f(n) = O(g(n)) means c.g(n) is an upper bound on f(n) such that f(n) is always ≤ c.g(n)
</blockquote>

I was going through basics of <a href="https://en.wikipedia.org/wiki/Big_O_notation" rel="nofollow noreferrer">Big-O</a> notation.

<blockquote>
 f(n) = Ω(g(n)) means c.g(n) is a lower bound on f(n) such that f(n) is always ≥ c.g(n)
 
 f(n) = O(g(n)) means c.g(n) is an upper bound on f(n) such that f(n) is always 
 ≤ c.g(n)
 for all n ≥ n0
</blockquote>

<a href="https://i.stack.imgur.com/x2at4.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/x2at4.png" alt="enter image description here"></a>

upper and lower bound is clear in graph above, but why is f(n) and upperbound intersecting? when its clear from above definition? does that have meaning or I am just pointing out unnecessarily?

Source: The Algorith Design Manual by Skiena

upper-bound intersecting unnecessarily

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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我正在学习符号的基础知识。f(n) =Ω(g(n))指的是f(n)上的下界，使得f(n)总是≥c.g(n)f(n) = O(g(n))指的是f(n)上的一个上界，使得f(n)总是所有n n0的≤c.g(n)​​上界和下界在上面的图中是清楚的，，但是为什么f(n)和上界相交？当它明确从上述定义？，这是有意义还是我只是指出...

问上界不必要地相交
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