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Fix LAAI3 asymptotic notation definition

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Tian Cheng (Riccardo) Xia
2024-03-04 09:49:48 +01:00
parent 622c686111
commit 81140bd62c
1 changed files with 2 additions and 2 deletions
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src/languages-and-algorithms-for-ai/module3/sections/_intro.tex
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@ -75,11 +75,11 @@
\begin{description}
\item[Big O] \marginnote{Big O}
A function $f: \mathbb{N} \rightarrow \mathbb{N}$ is $O(g)$ if $g$ is an upper bound of $f$.
\[ f \in O(g) \iff \exists \bar{n} \in \mathbb{N} \text{ such that } \forall n > \bar{n}, \exists c \in \mathbb{R}: f(n) \leq c \cdot g(n) \]
\[ f \in O(g) \iff \exists \bar{n} \in \mathbb{N} \text{ such that } \forall n > \bar{n}, \exists c \in \mathbb{R}^+: f(n) \leq c \cdot g(n) \]
\item[Big Omega] \marginnote{Big Omega}
A function $f: \mathbb{N} \rightarrow \mathbb{N}$ is $\Omega(g)$ if $g$ is a lower bound of $f$.
\[ f \in \Omega(g) \iff \exists \bar{n} \in \mathbb{N} \text{ such that } \forall n > \bar{n}, \exists c \in \mathbb{R}: f(n) \geq c \cdot g(n) \]
\[ f \in \Omega(g) \iff \exists \bar{n} \in \mathbb{N} \text{ such that } \forall n > \bar{n}, \exists c \in \mathbb{R}^+: f(n) \geq c \cdot g(n) \]
\item[Big Theta]\marginnote{Big Theta}
A function $f: \mathbb{N} \rightarrow \mathbb{N}$ is $\Theta(g)$ if $g$ is both an upper and lower bound of $f$.