L04 - Sets 1 Sets Informally A set is a collection...

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Sets 1
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Sets Informally : A set is a collection of (mathematical) objects, with the collection treated as a single mathematical object. real numbers, complex numbers, C integers, All students in our class Examples:
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Defining Sets Sets can be defined directly: e.g. {1,2,4,8,16,32,…}, {CSC1130,CSC2110,…} Order, number of occurence are not important. e.g. {A,B,C} = {C,B,A} = {A,A,B,C,B} A set can be an element of another set. {1,{2},{3,{4}}}
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Defining Sets by Predicates The set of prime numbers : ) { } ( | x A P x The set of elements , x , in A such that P ( x ) is true.
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Commonly Used Sets N = {0, 1, 2, 3, …}, the set of natural numbers Z = {…, -2, -1, 0, 1, 2, …}, the set of integers Z + = {1, 2, 3, …}, the set of positive integers Q = {p/q | p Z, q Z, and q 0}, the set of rational numbers R , the set of real numbers
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Special Sets Empty Set (null set) : a set that has no elements, denoted by ф or {}. Example: The set of all positive integers that are greater than their squares is an empty set. Singleton set : a set with one element Compare: ф and { ф } Ф : an empty set. Think of this as an empty folder { ф }: a set with one element. The element is an empty set. Think of this as an folder with an empty folder in it.
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