*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## One-To-One and Onto Functions

Some special types of mappings are the mappings of one-to-one and onto functions. A one-to-one correspondence is a type of function in which every object in the range is paired with, at most, one object from the domain. In other words, an object in the codomain can have no more than one arrow pointing to it. Example (b) is one-to-one, but example (a) is not one-to-one because both Albert and Bill play basketball; that is, basketball has two arrows pointing to it. Example (c) is the same as (b) except it also has football in the codomain; hence, it is a one-to-one correspondence because no element of the range has more than one arrow pointing to it.

An onto function has a relationship in which every object in the codomain is paired with at least one object in the domain. This means that one...

This section contains 722 words(approx. 3 pages at 300 words per page) |