# 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
• $\{1, 2, 3, 4, 8\} \supset \{1, 2, 3\}$