# One to One Correspondence

Pronunciation: /wʌn tu wʌn ˌkɔr.əˈspɒn.dəns/ Explain

A one to one correspondence between two sets exists if a mapping exists between the two sets such that each member of the first set maps to exactly one member of the second set and each member of the second set maps to exactly one member of the first set[2]. A one to one mapping is the same thing as a one to one correspondence. A correspondence that is one to one is also called injective.

### Examples of One to One Correspondence

• y = 2x is a one to one correspondence between two sets of real numbers (x, y): (-1,-2), (-0.5,-1), (0,0), (1,2), (3,6), ….
• The set of integers has a one to one correspondence to the set of even numbers.

### Examples of Mappings That are not One to One

• y = x2 is not a one to one correspondence between two sets of real numbers. Both x = -1 and x = 1 map to y = 1.
• The set of integers does not have a one to one correspondence to the set of real numbers.

### References

1. McAdams, David E.. All Math Words Dictionary, one to one correspondence. 2nd Classroom edition 20150108-4799968. pg 130. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Maddocks, J. R.. One-to-One Correspondence. jrank.org. Last Accessed 9/5/2018. http://science.jrank.org/pages/4861/One-One-Correspondence.html.
3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 49-50. www.archive.org. International Textbook Company. January 1963. Last Accessed 9/5/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n66/mode/1up/search/correspondence. Buy the book
4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 17. Thomson, Brooks/Cole. 2005. Last Accessed 9/5/2018. Buy the book

McAdams, David E. One to One Correspondence. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/o/onetoonecorrespondence.html.

### Revision History

4/27/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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