Symbols:O/Big-O Notation
Jump to navigation
Jump to search
Big-O Notation
- $\OO$
Used for example as follows in the context of sequences:
Let $g: \N \to \R$ be a real sequence, expressed here as a real-valued function on the set of natural numbers $\N$.
Then $\map \OO g$ is defined as:
- $\map \OO g = \set {f: \N \to \R: \exists c \in \R_{>0}: \exists n_0 \in \N: \forall n > n_0: 0 \le \size {\map f n} \le c \cdot \size {\map g n} }$
The $\LaTeX$ code for \(a_n = \map \OO {b_n}\) is a_n = \map \OO {b_n}
.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): $O$ and $o$ notation
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): O