# lecture18 - MA1100 Lecture 18 Functions Injective function...

This preview shows pages 1–9. Sign up to view the full content.

MA1100 Lecture 18 Functions Injective function Surjective function Bijection Chartrand: 9.3, 9.4

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

View Full Document
2 Injective function a b c d 1 2 3 A B g a b c d 1 2 3 A B f There are two elements in A that maps to a same element in B No two elements in A maps to a same element in B negation Lecture 18
3 Injective function a b c d 1 2 3 A B f Every pair of (different) elements in A have different images in B Formulate the statement mathematically " x, y œ A [If x y , then f(x) f(y)] Lecture 18

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

View Full Document
4 Injective function a b c d 1 2 3 A B f The function is called an injective function . We can also say: f is a one-to-one function f is an injection " x, y œ A [if x y , then f(x) f(y)] Definition Let f: A Ø B be a function from set A to set B. Suppose Lecture 18
5 Working definition " x, y œ A [if x y , then f(x) f(y)] If f: A Ø B is an injective function : Contrapositive " x, y œ A [if f(x) = f(y) , then x = y] If f: A Ø B is not an injective function : \$ x, y œ A such that [x y and f(x) = f(y)] Negation working definition Lecture 18 E.g. The sum-of-divisor function s is not injective.

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

View Full Document
6 Daily life examples Let A be the set of MA1100 students Let f: A Ø B Example (Daily life) B: set of student numbers f maps every student to his/her student number Let g: A Ø C C: set of all integers g maps every student to his/her MA1100 test score Let h: A Ø D D: set of mobile phone numbers h maps every student to his/her mobile number Lecture 18
7 Real function (Visualize) f: R Ø R defined by f(x) = 5x + 3 is injective . Example x y Visualization Plot the graph of the real function. Observe that any horizontal line intersects with the graph at exactly one point . This means every value on the y-axis corresponds to exactly one value on the x-axis. So f is an injective function. Lecture 18

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

View Full Document
8 Real function (formal argument) f: R Ø R defined by f(x) = 5x + 3 is injective . " x, y
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/15/2010 for the course MATHS MA1101R taught by Professor Vt during the Spring '10 term at National University of Singapore.

### Page1 / 34

lecture18 - MA1100 Lecture 18 Functions Injective function...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online