Odd Number

Pronunciation: /ɒd ˈnʌm bər/ Explain

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]

References

  1. odd. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 12/21/2009. 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. Last Accessed 2/1/2010. Buy the book

More Information

  • McAdams, David E.. Even Number. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/e/evennumber.html.

Cite this article as:

McAdams, David E. Odd Number. 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/o/oddnumber.html.

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Revision History

12/21/2009: Added "References". (McAdams, David E.)
1/4/2009: Changed equation to image. (McAdams, David E.)
8/26/2008: Added 'More Information'. (McAdams, David E.)
7/8/2008: Initial version. (McAdams, David E.)

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