11454
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Injective, Surjective, Bijective
In the function mapping
, the domain is all
values and the range is all
values.
If
implies
, the function is called injective, or one-to-one.
If for any
in the range there is an
in the domain so that
, the function is called surjective, or onto.
If both conditions are met, the function is called bijective, or one-to-one and onto.
Contributed by:
Ed Pegg Jr
SNAPSHOTS
RELATED LINKS
Bijection
(
Wolfram
MathWorld
)
Domain
(
Wolfram
MathWorld
)
Function
(
Wolfram
MathWorld
)
Injection
(
Wolfram
MathWorld
)
One-to-One
(
Wolfram
MathWorld
)
Range
(
Wolfram
MathWorld
)
Surjection
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Injective, Surjective, Bijective
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/InjectiveSurjectiveBijective/
Contributed by:
Ed Pegg Jr
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Bijective Mapping of an Interval to a Square
Tad Hogg
Horizontal and Vertical Line Tests
Ed Pegg Jr
Finding an Inverse
Ed Pegg Jr
Mapping a Square by Complex Functions
Chris Boucher
The Schwarzian Derivative of Iterated Functions
Benjamin Webb
Root Routes
John Kiehl
Function Transformations
Eric Schulz
Orbits of the Tent Function's Iterates
Bernard Vuilleumier
Graph of Inequalities
Ed Pegg Jr
How Triple Powers of Integers Begin and End
Ed Pegg Jr
Related Topics
College Mathematics
High School Finite Mathematics
High School Mathematics
High School Precalculus
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+