lecnotes6-1 - Lecture Notes, Concepts of Mathematics...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture Notes, Concepts of Mathematics (21-127) Lecture 1, Recitation AD, Spring 2008 6 Functions and Bijections 6.1 Functions READ: Textbook pages 125132. EXERCISES: Pages 153161, #117, 8185. Recall from your previous mathematical knowledge that a function assigns exactly one output to each input. This is a special type of relation: Definition 6.1 Let A and B be sets. A function f from A to B (or, from A into B ), de- noted f : A B , is a relation from A to B that satisfies (i) Dom ( f ) = A (ii) If ( x,y ) f and ( x,z ) f , then y = z . In the case where A = B , we say f is a function on A . The function f is also called a mapping . We also refer to B as the codomain of f . Note that Rng( f ) is a subset of the codomain of f . The element y = f ( x ) B is called the value of f at x A or the image of x under f , y is the depenedent variable . x is a pre-image of y under f and is the independent variable or argument of f . We may also consider the action of f on a set, i.e., f ( A ) = Rng( f ). Note: To verify that a given relation f from A to B is a function from A to B , it must be shown that every element of A appears as a first coordinate of exactly one ordered pair in...
View Full Document

Page1 / 3

lecnotes6-1 - Lecture Notes, Concepts of Mathematics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online