Introduction to Set Notations

• Universal set \({\xi}\) is the set of all elements under consideration.
• \({\in}\) means ‘is an element of’.
• \({\notin}\) means ‘is not an element of’.
• Set notation by listing all elements in the set, e.g. \({A = \{1, 3, 4, 5\}}\).
• Set notation by Set-builder form, e.g. \({A = \{(x,y)\in\mathbb R^2:y=x+1\}}\), \({A = \{x \in \mathbb{R} : x \leq 3\}}\).
• \({\mathrm{n}(A)}\) means the number of the elements in the set \({A}\), also known as the ‘size of the set \({A}\)’, the ‘cardinality of the set \({A}\)’.
• Equal set contain exactly the same elements. E.g. \({A = \{1, 3, 4, 5\}}\), \({B = \{5, 3, 4, 1\}}\), thus \({A = B}\) and \({\mathrm{n}(A) = \mathrm{n}(B)}\).
• The empty or null set is the set containing no element. E.g. \({A = \{ \quad \}}\) or \({A = \varnothing}\).
• Finite set: A set that contains finite number of elements; Infinite set: A set that contains infinite number of elements.
• Elements of any set are certain, unique, and orderless.