Наставни материјали

Скупови бројева

$$ \begin{align*} & \begin{aligned} \mathbb N = \lbrace 1, 2, 3, 4, ... \rbrace \end{aligned} \qquad \begin{aligned} \mathbb Z = \lbrace ..., -3, -2, -1, 0, 1, 2, 3, ... \rbrace \end{aligned} \\ & \begin{aligned} \mathbb Q = \left\lbrace \frac ab \mathop{\Big|} a \in \mathbb Z \land b \in \mathbb N \right\rbrace \end{aligned} \qquad \begin{aligned} \mathbb R = (-\infty, \infty) \end{aligned} \\ & \begin{aligned} \mathbb N \subset \mathbb Z \subset \mathbb Q \subset \mathbb R \end{aligned} \end{align*} $$

Затвореност за операције

$$ \begin{align*} & (\mathbb N, +) \quad (\mathbb N, \cdot) \\ & (\mathbb Z, +) \quad (\mathbb Z, -) \quad (\mathbb Z, \cdot) \\ & (\mathbb Q, +) \quad (\mathbb Q, -) \quad (\mathbb Q, \cdot) \quad (\mathbb Q \setminus {0}, :) \\ & (\mathbb R, +) \quad (\mathbb R, -) \quad (\mathbb R, \cdot) \quad (\mathbb R \setminus {0}, :) \quad (\mathbb R^+ \cup {0}, \surd) \end{align*} $$