mirror of
https://github.com/Steffo99/appunti-magistrali.git
synced 2024-11-24 11:14:18 +00:00
30 lines
636 B
Markdown
30 lines
636 B
Markdown
---
|
|
aliases:
|
|
- omega-piccola
|
|
- small-ω
|
|
- small-omega
|
|
---
|
|
[[notazione asintotica]] per il [[limite inferiore]].
|
|
|
|
$$
|
|
\def \varAsym {{\color{royalblue} g(n)}}
|
|
\def \varFunc {{\color{orangered} f(n)}}
|
|
\def \varLess {{\color{lightcoral} c_{less}}}
|
|
\def \varBeginning {{\color{turquoise} n_0}}
|
|
\Huge
|
|
\omega(\varAsym)
|
|
$$
|
|
In linguaggio formale, $\varFunc$ è in $\omega(\varAsym)$ se:
|
|
$$
|
|
\omega(\varAsym)
|
|
\Longleftrightarrow
|
|
\begin{cases}
|
|
\forall & \varLess > 0\\
|
|
\\
|
|
: & \begin{cases}
|
|
\exists & \varBeginning > 0\\
|
|
\forall & n \geq \varBeginning\\
|
|
: & 0 \leq (\varLess \cdot \varAsym) \leq \varFunc
|
|
\end{cases}
|
|
\end{cases}
|
|
$$
|