# Odd Number

Pronunciation: /ɒd ˈnʌm.bər/ Explain

An integer is odd if it is not evenly divisible by 2.[2] 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 ∈ ℤ}, { …, -3, -1, 1, 3, 5, … }

### Properties of odd numbers

• The sum of two odd numbers is an even number.[3]
• The sum of two consecutive numbers is always odd.[3]
• The sum of an even and an odd number is always odd.[3]

### References

1. McAdams, David E.. All Math Words Dictionary, odd number. 2nd Classroom edition 20150108-4799968. pg 129. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. odd. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 9/5/2018. http://www.merriam-webster.com/dictionary/odd. Buy the book
3. 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 9/5/2018. Buy the book

• 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.

McAdams, David E. Odd Number. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/o/oddnumber.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.)