Category:Definitions/Little-O Notation
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This category contains definitions related to little-$\oo$ notation.
Related results can be found in Category:Little-O Notation.
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:
- $\map \oo g = \set {f: \N \to \R: \forall c \in \R_{>0}: \exists n_0 \in \N: \forall n > n_0: \size {\map f n} \le c \cdot \size {\map g n} }$
Estimate at Infinity
Let $f$ and $g$ be real functions defined on a neighborhood of $+\infty$ in $\R$.
Let $\map g x \ne 0$ for $x$ sufficiently large.
$f$ is little-$\oo$ of $g$ as $x \to \infty$ if and only if:
- $\ds \lim_{x \mathop \to \infty} \frac {\map f x} {\map g x} = 0$
Pages in category "Definitions/Little-O Notation"
The following 15 pages are in this category, out of 15 total.
L
- Definition:Landau Symbols
- Definition:Little-O Estimate for Real Function
- Definition:Little-O Estimate for Real Function at Infinity
- Definition:Little-O Notation
- Definition:Little-O Notation for Sequences
- Definition:Little-O Notation/Also known as
- Definition:Little-O Notation/General Definition/Point
- Definition:Little-O Notation/Real
- Definition:Little-O Notation/Real/Infinity
- Definition:Little-O Notation/Real/Infinity/Definition 1
- Definition:Little-O Notation/Real/Infinity/Definition 2
- Definition:Little-O Notation/Sequence
- Definition:Little-O Notation/Sequence/Definition 1
- Definition:Little-O Notation/Sequence/Definition 2
- Definition:Little-O Notation/Sequence/Informal Definition