29-Functions

29-Functions - Discussion #29 Chapter 6, Sections 6.1-7...

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Unformatted text preview: Discussion #29 Chapter 6, Sections 6.1-7 1/18 Discussion #29 Functions Discussion #29 Chapter 6, Sections 6.1-7 2/18 Topics • Function Definition • Notation • Partial Functions • Restrictions • Overloading • Composition • Injections, surjections, bijections • Inverses Discussion #29 Chapter 6, Sections 6.1-7 3/18 • A function is a special kind of binary relation. • A binary relation f ⊆ A × B is a function if for each a ∈ A there is a unique b ∈ B Function Definition 1 2 3 α β γ x y Discussion #29 Chapter 6, Sections 6.1-7 4/18 NOT Functions 1 2 3 α β γ f = {(1, α), (2, β)} “For each” violated Some x’s do not have corresponding y’s x y Discussion #29 Chapter 6, Sections 6.1-7 5/18 NOT Functions Uniqueness violated for some x’s x y 1 2 3 α β γ f = {(1, α), (2, β), (3, β), (3, γ)} uniqueness violated for 3 appears twice Discussion #29 Chapter 6, Sections 6.1-7 6/18 An (n+1)-ary relation f ⊆ A 1 × A 2 × … × A n × B is a function if for each < a 1 , a 2 , …, a n > ∈ A 1 × A 2 × … × A n there is a unique b ∈ B. Functions with N-Dimensional Domains α β γ <1,1> <1,2> <1,3> Discussion #29 Chapter 6, Sections 6.1-7 7/18 • We can use various notation for functions: for f = {(1, α),(2, β),(3, β)} Notation for Functions Notation (x, y) ∈ f f : x→y...
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This note was uploaded on 03/02/2012 for the course C S 236 taught by Professor Michaelgoodrich during the Winter '12 term at BYU.

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29-Functions - Discussion #29 Chapter 6, Sections 6.1-7...

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