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handout4 - ECS20 Handout 4 1 A function f from set A to set...

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Unformatted text preview: ECS20 Handout 4 January 11, 2011 1. A function f from set A to set B is an assignment of exactly one element of B to each element of A . notation: f : A → B, f ( a ) = b A is called the domain of f , and B is codomain . The set { f ( a ) | a ∈ A } is called the range of f . 2. f : A → B is one-to-one , or injective , if f ( a ) = f ( b ), then a = b . Examples: 1 • Is the function f : Z → Z , f ( x ) = x 2 one-to-one? • Is the function f : { US residents } → Z , f ( x ) = SSN one-to-one? 3. f : A → B is onto , or surjective , if for any b ∈ B , there is an a ∈ A with f ( a ) = b . Examples: • Is the function f : Z → Z , f ( x ) = x 2 onto? • Is the function f ( x ) = x + 1 from Z to Z onto? 4. f is one-to-one correspondence , or a bijection , if it is both one-to-one and onto. Examples: • Is f ( x ) = x + 1 from Z to Z bijective? • The identity function ℓ A : A → A , ℓ A ( x ) = x , is a bijection....
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handout4 - ECS20 Handout 4 1 A function f from set A to set...

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