I have a question with respect to the Big Oh notation, in which the Landau symbol [tex]O(n)[/tex] is involved.(adsbygoogle = window.adsbygoogle || []).push({});

The Landau symbol [itex]O(n)[/itex] is defined as:

[tex]f(n)=O(g(n))[/tex] if there exists an integer [tex]n_0[/tex] and a constant [tex]C>0[/tex]

such that for all integers [tex]n \geq n_0[/tex], [tex]f(n) \leq C \cdot g(n)[/tex].

For example [tex]f(n)= 5 \cdot n = O(n)[/tex].

Now the equality sign is not to be understand as an equality sign in the common sense, but rather as [tex]f(n) \in O(n)[/tex], see Big Oh Fallacies and Pitfalls and

the Wikipedia article.

( [itex]5 \cdot n = O(n)[/itex] and [itex]2 \cdot n = O(n)[/itex], but [itex] 5 \cdot n \neq 2 \cdot n[/itex])

So it would be better to think of [tex]O(n)[/tex] as a set of functions.

My question:

Does anyone know why it became common to use the notation f(n)=O(g(n))?

I remember my professor mentioning that physicists introduced this sloppy notation.

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# Big Oh notation (Landau symbols)

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