diff --git a/src/languages-and-algorithms-for-ai/module3/sections/_intro.tex b/src/languages-and-algorithms-for-ai/module3/sections/_intro.tex index bbb4cc8..792f391 100644 --- a/src/languages-and-algorithms-for-ai/module3/sections/_intro.tex +++ b/src/languages-and-algorithms-for-ai/module3/sections/_intro.tex @@ -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 $f$.