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30 lines
636 B
Markdown
30 lines
636 B
Markdown
---
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aliases:
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- omega-piccola
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- small-ω
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- small-omega
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---
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[[notazione asintotica]] per il [[limite inferiore]].
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$$
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\def \varAsym {{\color{royalblue} g(n)}}
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\def \varFunc {{\color{orangered} f(n)}}
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\def \varLess {{\color{lightcoral} c_{less}}}
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\def \varBeginning {{\color{turquoise} n_0}}
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\Huge
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\omega(\varAsym)
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$$
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In linguaggio formale, $\varFunc$ è in $\omega(\varAsym)$ se:
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$$
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\omega(\varAsym)
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\Longleftrightarrow
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\begin{cases}
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\forall & \varLess > 0\\
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\\
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: & \begin{cases}
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\exists & \varBeginning > 0\\
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\forall & n \geq \varBeginning\\
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: & 0 \leq (\varLess \cdot \varAsym) \leq \varFunc
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\end{cases}
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\end{cases}
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$$
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