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
  • \(\{1, 2, 3, 4, 8\} \supset \{1, 2, 3\}\)