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I am learning from the MIT course Introduction to Algorithms.

The professor says:

Now, remember $\Theta(n)$ is essentially something that says "of the order of $n$".

What does "of the order of $n$" mean? Are "of the order of $n$" and "Big O" the same thing?

Please provide the name of any widely recognized textbook that contains detailed explanation about this.

dkaeae
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brennn
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2 Answers2

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"On the order of" is an informal statement which really only means "approximately". Big O notation is a precise mathematical formulation which expresses asymptotic behavior, not approximate values of a function (e.g., $10n \in O(n)$, despite $10n$ being 10 times as larger as $n$). They can hardly be considered the same things. What the lecturer is trying to do here is supposedly give you some (hand-wavy) intuition as to how Big O notation works, but that should not replace you actually sitting down and learning the precise definitions.

As for your request regarding further reading on Big O notation, (in addition to the linked Wikipedia article) I suggest you take a look at our reference question.

An addendum: After listening to the video again, you can make out the lecturer say "of the order of $n$". This is the British English version of American English "on the order of" and carries the same meaning.

dkaeae
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the professor mentioned two methods used to measure asymptotic complexity.

$\Theta(n)$ is the order of n.

$O(n)$ is big O of n.

the professor explained

$\Theta(n)$

gives you both the lower bound and an upper bound.

$O(n)$

is just upper bound.

Sasha
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JJJohn
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