Pronunciation of the big-O notation

How should I pronounce the following things? (These are complexities of algorithms.)

• O(n)
• O(n*log(n))
• O(n^2)
• This question is more appropriate for math.stackexchange.com or cstheory.stackexchange.com. Jun 1, 2011 at 16:28
• @Mitch cstheory is for research level questions only, see cstheory.stackexchange.com/faq Jun 2, 2011 at 18:25
• I think this is a pointless question. Does OP really want to know whether O is pronounced as Owe rather than Big Oh? Or maybe it should be pronounced zer-OWE? I'm voting to close, and if I could delete it I would do that. Jun 23, 2011 at 3:06

Pronunciation would be:

• order n
• order n log n
• order n squared
• If the context (of computational order) is already established, I've also heard "o of n" (etc). Jun 1, 2011 at 16:38
• Its just known as the 'Big O' in my discrete math class. aka the maximum amount of times an algorithm will be run. Jun 23, 2011 at 2:56

In the talks I've seen that involve algorithm complexity, I've heard it most often pronounced "oh of n", "oh of n log n", etc.

Mathematicians and CS theorists also use a lowercase o and a capital ϴ for similar measurements with slightly different implications. In this case O( n ) would be pronounced "big oh of n", o( n ) "little oh of n", and ϴ(n) "theta of n".

• A footnote on the Wikipedia article says O(g(n)) is pronounced "big-oh of g of n" or sometimes just "oh of g of n", referencing Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L. (2009). Introduction to Algorithms (3rd ed.). Cambridge/MA: MIT Press. p. 47. Aug 24, 2022 at 12:01
• @StuartF: Thanks for adding the reference! Aug 24, 2022 at 13:42

That is commonly referred to as Big O Notation, and since my days as a math/CS student I have always pronounced it (and heard it pronounced) as "Big O of n", "Big O of n log n", etc.

I think it's also common to just say "oh" followed by whatever is inside the parentheses.

Examples:

There is an "oh n log n" algorithm for that problem

Doesn't that require "oh n squared" time in the worst case?

The ‚Θ -notation asymptotically bounds a function from above and below. When we have only an asymptotic upper bound, we use O-notation. For a given function g(n), we denote by O(g(n)) (pronounced “big-oh of g of n” or sometimes just “oh of g of n”) the set of functions

O(g(n)) = { f(n): there exist positive constants c and n0 such that 0 ≤ f(n) ≤ c.g(n) for all n ≥ n0}

ref: Introduction to Algorithms, fourth edition

• This was probably unneeded. It does not tell us anything new about the question ("pronunciation"); and furthermore it has been more than 10 years. Aug 24, 2022 at 10:11