Criterion

Pronunciation: /kraɪˈtɪər.iən/ Explain

A criterion is a necessary requirement for a theorem to be true. When a standard is given to show what members are included in a set, the standard is called a criterion. The plural of criterion is criteria.

Example:

If only high school students can participate in a math contest, the criterion for participating in the math contest is being a high school student.

Understanding Check

For each of the statements below identify the criterion. The click on the answer you picked.

• If x < 0 then y > 0.
  A. x < 0 A. Correct. Since x < 0 is the condition, it is the criterion. B. y > 0 B. Incorrect. x < 0 is the condition, so it is the criterion.
• When your room is cleaned up, you can go to the mall.
  A. Your room is cleaned up. A. Correct. Since the condition for going to the mall is cleaning your room, 'Your room is cleaned up' is the criterion. 'You can go to the mall,' is what happens after the criterion is met. B. You can go to the mall. B. Incorrect. 'You can go to the mall' is what happens after the condition or criterion is met. The criterion is 'Your room is cleaned up'.
• We will stay inside if it is raining.
  A. We will stay inside. A. Incorrect. Staying inside is what happens if the criterion 'it is raining' is met. 'It is raining' is the criterion. B. It is raining. B. Correct. 'It is raining' is the criterion. Going outside is what happens if the criterion is met, so 'It is raining' is the criterion.
• If the shirt fits and we can afford it, we will buy the shirt.
  A. The shirt fits. A. Correct. 'The shirt fits' is a criterion for buying the shirt. However, it is not the only criterion. See if you can identify the other criterion. B. We can afford the shirt. B. Correct. 'We can afford the shirt' is a criterion for buying the shirt. However, it is not the only criterion. See if you can identify the other criterion. C. We will buy the shirt. C. Incorrect. 'We will buy the shirt' is what happens if the criteria are met. The criteria are 'The shirt fits' and 'We can afford the shirt'.

References

1. McAdams, David E.. All Math Words Dictionary, criterion. 2nd Classroom edition 20150108-4799968. pg 50. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

• McAdams, David E.. condition. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. https://www.allmathwords.org/en/c/condition.html.

Cite this article as:

McAdams, David E. Criterion. 4/16/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/criterion.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/16/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/6/2010: Added "References". (McAdams, David E.)
7/11/2008: Added Understanding Check. (McAdams, David E.)
3/25/2008: Revised More Information to match current standard. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)