This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Discussion #29 Chapter 6, Sections 6.17 1/18 Discussion #29 Functions Discussion #29 Chapter 6, Sections 6.17 2/18 Topics • Function Definition • Notation • Partial Functions • Restrictions • Overloading • Composition • Injections, surjections, bijections • Inverses Discussion #29 Chapter 6, Sections 6.17 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 6.17 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 6.17 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 6.17 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 NDimensional Domains α β γ <1,1> <1,2> <1,3> Discussion #29 Chapter 6, Sections 6.17 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...
View
Full
Document
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.
 Winter '12
 MichaelGoodrich

Click to edit the document details