Set Notation

Tyler MurphyLearning Assistant en Boise State University

Some notes for Math 189, BSU, spring 2014

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Set Notation

• 1. Set Notation Tyler Murphy February 12, 2014 Symbol A | : ∈ ∈ / ∪ ∩ ⊆ ⊂, , ∅ |S| Meaning Denotes the name of the Set Such that Such that Is an element of Is not an element of union of two sets (all elements in A or B) intersection of two sets (elements in A AND B only) union of multiple sets intersection of multiple sets is a subset of is a proper subset of (not equal to) [all are equivalent notation] The empty set The size of S. (The cardinality of S) Usage A = {1, 2, 3...} A = {x | x is even} A = {x : x is odd} x∈A x∈A / A∪B A∩B ∞ n=1 An ∞ n=1 Bn A⊆B A⊂B ∅ = {} S = {1, 2, 3}.|S| = 3. Also, when thinking about elements of sets versus subsets of sets, consider this. Deﬁne a building as a set with all the people in the building as the elements of that set. Now think of the university as a set of all the buildings on campus. The elements of the university are buildings. The subsets of the university are groups of those buildings. However, the people in the buildings are not elements or subsets of the collection of buildings. They are elements of the buildings, though. Consider U = {math building, ILC, Library, Ed Building, SMTC, MECB}. and MECB = {people in the MECB }. Note that MECB ∈ U . And {MECB} ⊂ U . The diﬀerence in these statements is subtle but profound. For something to be a subset, it must be wrapped in set brackets. In this thought line it is clear that MECB ⊂ U is false. It is an element but not a subset because it is not a set. It is simply an object whereas {MECB} is a set with one object in it. 1
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