Order

Pronunciation: /ˈɔr.dər/ Explain

The order of a set is how the set is sorted.^[2] One example of an ordered set is the set of integers. One can always tell which of any two integers come first. For example, 1 always comes before 5.

The operators =, ≠, <, >, ≤, ≥ show the relative order of elements of an ordered set.

Sets other than numbers can be ordered. For example, the alphabet is an ordered set of letters. The statement 'a' < 'd' makes sense in terms of this ordering.

The points in a line are ordered. One can tell which points come before and after a particular point.

References

1. McAdams, David E.. All Math Words Dictionary, order. 2nd Classroom edition 20150108-4799968. pg 131. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Hilbert, David. The Foundations of Geometry. pg 3. Translated by Townsend, E. J., Ph. D.. The Open Court Publishing Company. 1950. Last Accessed 9/5/2018. http://www.gutenberg.org/files/17384/17384-pdf.pdf. Buy the book

Cite this article as:

McAdams, David E. Order. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/o/order.html.

Revision History

4/27/2019: Changed equations and expressions to new format. (McAdams, David E.)
3/26/2019: Clarified wording. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/5/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
12/21/2009: Added "References". (McAdams, David E.)
4/25/2008: Initial version. (McAdams, David E.)