You are here:

Advanced Math/function in math

Advertisement

Expert: Sherry Wallin - 1/19/2009


Question
sherry please teach me the surjective,injective,bijective function .please teach me

Answer

diagram of injective a
Pratap~
    I will try to explain these terms in simpler but less elegant mathematical vocabulary.

The easiest to define is that bijective is a function that is both injective and surjective. [Of course this will do you no good until you understand injective and surjective but that is what I will tell you next]. Bijective can also be said to be a one to one correspondence.

Another word for an injective function is a function that is one-to-one.
Recall I told you one interpretation of a function is ordered pairs on an x-y coordinate system (x,y) and I also told you that in an equation in x and y you could solve for the y and think of f(x) as being y. Being one-to-one means simply that in a function of x, every x is mapped to a distinct y. In other words you can not have the ordered pairs (2,3) and (1,3) in a one-to-one because both x = 1 and x = 2 are functionally mapped to f(x) = y = 3. An example of a non- one-to-one function is f(x) = x^2 and using f(x) = 9, both x =3 and x=-3 gives us y = 9 or f(x) = 9. Since 3 and -3 are mapped to the same y this function is not one-to-one or injective.

Surjective is another word for the idea of 'onto'. Onto means simply that whatever set f(x) is that every element in that set gets an element from the set that contains x mapped to it. You can think of onto as being every element in f(x) is hit as in a target. An example of a function that is not onto or surjective is suppose the set A (these are your x values)consists of {2,3} and the set B is {-1,1} (these are your y or f(x) values) and your function is f(x) = x^0.[If you don't know this, any number raised to the 0 power has a value of 1]. So both 2^0 and 3^0 = 1. Notice that neither functional value takes on -1 so the target -1 is not 'hit'.

I will attached a visual representation of what I have shown.

Back to bijective or one to one correspondence:
Each and every x is mapped to a unique y and every y is hit. This makes the set that contains x and the set that contains y the same size.


Math Prof

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

©2012 About.com, a part of The New York Times Company. All rights reserved.