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Big Omega notation

Another asymptotic notation is Ω {\displaystyle \Omega }, read "big omega". There are two widespread and incompatible definitions of the statement

where a is some real number, ∞ {\displaystyle \infty }, or − ∞ {\displaystyle -\infty }, where f and g are real functions defined in a neighbourhood of a, and where g is positive in this neighbourhood.

The Hardy–Littlewood definition is used mainly in analytic number theory, and the Knuth definition mainly in computational complexity theory; the definitions are not equivalent.