Multiple Variables
Big O (and little o, and Ω...) can also be used with multiple variables. To define Big O formally for multiple variables, suppose and are two functions defined on some subset of . We say
if and only if
For example, the statement
asserts that there exist constants C and M such that
where g(n,m) is defined by
Note that this definition allows all of the coordinates of to increase to infinity. In particular, the statement
(i.e., ) is quite different from
(i.e., ).
Read more about this topic: Big O Notation
Famous quotes containing the words multiple and/or variables:
“... the generation of the 20’s was truly secular in that it still knew its theology and its varieties of religious experience. We are post-secular, inventing new faiths, without any sense of organizing truths. The truths we accept are so multiple that honesty becomes little more than a strategy by which you manage your tendencies toward duplicity.”
—Ann Douglas (b. 1942)
“The variables are surprisingly few.... One can whip or be whipped; one can eat excrement or quaff urine; mouth and private part can be meet in this or that commerce. After which there is the gray of morning and the sour knowledge that things have remained fairly generally the same since man first met goat and woman.”
—George Steiner (b. 1929)