# Notations

$$[x]_{+} = max(0, x)$$

• $$\Omega$$ - universal set(set that contain all objects)
• $$\in$$ - is member of
• $$2 \in \{1, 2, 3, 4\}$$
• $$\notin$$ - is not member of
• $$2 \notin \{1, 3, 5\}$$
• $$A’$$, $$A^c$$, $$\overline{\rm A}$$ - $$A$$ compliment, everything not in $$A$$
• $$x \in S^c if x \in \Omega, x \notin S$$
• $$\emptyset$$ and $$\varnothing$$ or $$\{ \}$$ - empty set
• $$\Omega^c = \emptyset$$
• $$\cup$$ - union, everything in both sets
• $$\{1, 2, 3\} \cup \{3, 4, 5\} = \{1, 2, 3, 4, 5\}$$
• $$x \in S \cup T \leftrightarrow x \in S \, \textsf{or} \> x \in T$$
• $$\cup_{n} S_{n}$$ - union of all $$n$$ sets
• $$\cap$$ - intersection, only what is in common in both sets
• $$\{1, 2, 3\} \cap \{2, 3, 4\} = \{2, 3\}$$
• $$x \in S \cap T \leftrightarrow x \in S \, \textsf{and} \, x \in T$$
• $$\cap_{n} S_{n}$$ - intersection of all $$n$$ sets
• $$\subset$$ - subset of set
• $$\{1, 2, 3\} \subset \{1, 2, 3, 4, 8\}$$
• $$\supset$$ - superset of set
• $$\{1, 2, 3, 4, 8\} \supset \{1, 2, 3\}$$