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section05 - Sets and Functions Sets and Functions If there...

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Unformatted text preview: Sets and Functions Sets and Functions If there is one unifying foundation common to all branches of mathematics, it is the theory of sets. MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Sets and Functions Sets and Functions If there is one unifying foundation common to all branches of mathematics, it is the theory of sets. The idea of set is very intuitive. For example we speak of 1 a football team MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Sets and Functions Sets and Functions If there is one unifying foundation common to all branches of mathematics, it is the theory of sets. The idea of set is very intuitive. For example we speak of 1 a football team 2 a flock of geese MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Sets and Functions Sets and Functions If there is one unifying foundation common to all branches of mathematics, it is the theory of sets. The idea of set is very intuitive. For example we speak of 1 a football team 2 a flock of geese 3 a doctoral committee MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Sets and Functions Sets and Functions If there is one unifying foundation common to all branches of mathematics, it is the theory of sets. The idea of set is very intuitive. For example we speak of 1 a football team 2 a flock of geese 3 a doctoral committee Definition A set is a collection of objects characterized by some defining property. The objects in a set are called elements or members of the set. We use capital letters to designate sets, lowercase letters to designate elements and the symbol 2 to denote membership in a set, and a = 2 B means a is not an element of B . MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Sets and Functions Sets and Functions For example, MAT 300 Awtrey MATHEMATICS AND STATISTICS 2 / 28 Sets and Functions Sets and Functions For example, If A = f 1 ; 2 ; 3 ; 4 g , then 2 2 A and 5 = 2 A . MAT 300 Awtrey MATHEMATICS AND STATISTICS 2 / 28 Sets and Functions Sets and Functions For example, If A = f 1 ; 2 ; 3 ; 4 g , then 2 2 A and 5 = 2 A . To say that a set must be characterized by some defining property is to require that it be a clear question of fact whether a particular object does or does not belong to a particular set. MAT 300 Awtrey MATHEMATICS AND STATISTICS 2 / 28 Sets and Functions Sets and Functions For example, If A = f 1 ; 2 ; 3 ; 4 g , then 2 2 A and 5 = 2 A . To say that a set must be characterized by some defining property is to require that it be a clear question of fact whether a particular object does or does not belong to a particular set. Said another way, we require that the sentence “ a 2 A ” be a statement: MAT 300 Awtrey MATHEMATICS AND STATISTICS 2 / 28 Sets and Functions Sets and Functions For example, If A = f 1 ; 2 ; 3 ; 4 g , then 2 2 A and 5 = 2 A ....
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section05 - Sets and Functions Sets and Functions If there...

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