Odd Number

Pronunciation: /ɒd ˈnʌm bər/ ?

A number is odd if it is not evenly divisible by 2.[1] Expressed mathematically, odd integers are in the form 2k+1 where k is an integer. In set notation, odd integers are {x|x=2k+1, k in Z} = {..., -3, -1, 1, 3, 5, ...}

Properties of odd numbers

  • The sum of two odd numbers is an even number.[2]
  • The sum of two consecutive numbers is always odd.[2]
  • The sum of an even and an odd number is always odd.[2]


  1. odd. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-12-21). http://www.merriam-webster.com/dictionary/odd.
  2. Antonella Cupillari. The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs, 3rd edition, pg 12. # Academic Press, June 3, 2005. (Accessed: 2010-02-01).

More Information

  • McAdams, David. Even Number. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Even%20Number.
  • Even and Odd Numbers. aaamath.com. 2009-03-12. http://www.aaamath.com/g25a2-evenodd.html.

Printed Resources

Cite this article as:

Odd Number. 2009-12-21. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/o/oddnumber.html.


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Revision History

2009-12-21: Added "References" (McAdams, David.)
2009-01-04: Changed equation to image (McAdams, David.)
2008-08-26: Added 'More Information' (McAdams, David.)
2008-07-08: Initial version (McAdams, David.)

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