# Lecture Notes for CSC 500 - Discrete Structures at SUNY Institute of Technology at Utica-Rome (SUNY IT)

## Notes Information

 Material Type: Class Note Professor: Staff Class: CSC 500 - Discrete Structures Subject: Computer Science University: SUNY Institute of Technology at Utica-Rome Term: -- Keywords: CombinationsDefinitionsConvergenceOne-to-One CorrespondenceBinary SearchBubble Sort

## Sample Document Text

Functions. A mapping. Usual notation If a ∈ A , f ( a ) = b ∧ b ∈ B f: A → B a b c A B d y x m z All members of A are mapped to the set B. A is the domain of the function f, B, its range or codomain. Functions as relations. Composite functions. f: A→B and then g: B→C is a mapping g*f such that g*f: A → C. One-to-0ne, Onto function A function f: A → B is one-to-one if all its members are mapped, and different members of A are mapped to different members in B. Also called injective functions. A function is onto if all elements of B are images of some elements of A. a m o n p An onto function is also called a surjective function. A function that is both one-to-one and onto are called bijective functions or a one-to-one correspondence. General features of one-to-one and onto functions For an one-to-one f: A → B we cannot have distinct pairs (a,b), (c,b). b c No horizontal line can intersect f at more than one points. For an onto function, ∀b ∈ B , ∃a ∈ A such that ( a , b ) belongs...