MATH 110 Lecture Notes - Lecture 10: Null Set, Subset, Empty Set
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A set is a group of objects, numbers, and so forth. {1,2,3} is a set consisting of the numbers 1,2, and 3. Verbally, (cid:1688)3 is an element of the set {1,2,3}. (cid:1689) to show this symbolically, use the symbol , which is read as (cid:1688)is an element of(cid:1689) or (cid:1688)is a member of. (cid:1689) A subset is a set contained within another set, or it can be the entire set itself. {1,2} is a subset of the set {1,2,3}, and the set {1,2,3} is a subset of the set {1,2,3}. When the subset is missing some elements that are in the set it is being compared to, it is a proper subset. when the subset is the set itself, it is an improper subset. The symbol used to indicate (cid:1688)is a proper subset of(cid:1689) is . When there is the possibility of using an improper subset, the symbol used is . Therefore, {1,2} {1,2,3} and {1,2,3} or members.