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# big-O

Suppose f(*x*) and g(*x*) are real valued
functions defined for all *x* greater than some fixed positive real *x*_{0}.
We write

f(x) = O(g(x)) (and we say "f(x) isbig-Oof g(x)"),

if there is some constant C such that

|f(x)| < C^{.}g(x)

That is, f(*x*) is O(g(*x*)) if f is bounded
by a constant times g.

For example,
53*x*^{2}+23*x*+500 =
O(*x*^{2}), sin(*x*) = O(1), and
any polynomial in *x* of degree at most
*n* is O(*x*^{n}).

This big-O notation was introduced by P. Brachmann in 1894.

**See Also:** LittleOh, SameOrderofMagnitude, AsymptoticallyEqual

**References:**little-o, same order of magnitude, asymptotically equal

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