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)
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)