I came across several forums and articles saying that criteria is plural and criterion is singular. Some gave me the impression that criterion is used to denote a set of rules.
What is the correct use of these two words?
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According to Merriam-Webster.com, criteria is indeed plural and criterion is singular. The dictionary definition is "a standard on which a judgement or decision may be made"; it's often used synonymously with "requirement(s)", as in "if you don't meet the criteria you won't be allowed in" or "I have one all-important criterion by which I judge potential plumbing contractors: is their shirt tucked in to their belted pants?"
M-W.com also notes that the use of "criteria" as singular has been gaining ground for a long time (50 years or so) and may be considered acceptable usage by now.
(To which I say, fight the change! Use "criterion" correctly!)
In English, a lot of nouns have kept the original ending coming from classical Greek or Latin. Criterion is just one of them. In science you find a lot of words with these queer plural forms, but in fact they follow the Greek and latin declensions: Latin: alga- algae stimulus -stimuli bacterium -bacteria species-speciei (except that this one is no longer used, it has been replaced by species, due to the fact that in several modern languages "s" means plural. Greek: a thesis -2 theses an analysis -two analyses a criterion -two criteria
This means that if you know the singular form in "a" or "us" or "um", you can deduce the plural !!