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Linguistic prescriptivists usually say that fewer and not less should be used with countable nouns, [2] and that less should be used only with uncountable nouns. This distinction was first tentatively suggested by the grammarian Robert Baker in 1770, [ 3 ] [ 1 ] and it was eventually presented as a rule by many grammarians since then.
The concept of a "mass noun" is a grammatical concept and is not based on the innate nature of the object to which that noun refers. For example, "seven chairs" and "some furniture" could refer to exactly the same objects, with "seven chairs" referring to them as a collection of individual objects but with "some furniture" referring to them as a single undifferentiated unit.
The determinative function is typically obligatory in a singular, countable, common noun phrase (compare I have a new cat to *I have new cat). Semantically , determiners are usually definite or indefinite (e.g., the cat versus a cat ), [ 4 ] and they often agree with the number of the head noun (e.g., a new cat but not * many new cat ).
In linguistics, a mass noun, uncountable noun, non-count noun, uncount noun, or just uncountable, is a noun with the syntactic property that any quantity of it is treated as an undifferentiated unit, rather than as something with discrete elements. Uncountable nouns are distinguished from count nouns.
Mass nouns or uncountable (non-count) nouns differ from count nouns in precisely that respect: they cannot take plurals or combine with number words or the above type of quantifiers. For example, the forms a furniture and three furnitures are not used – even though pieces of furniture can be counted.
The term measure word is also sometimes used to refer to numeral classifiers, which are used with count nouns in some languages. For instance, in English no extra word is needed when saying "three people", but in many East Asian languages a numeral classifier is added, just as a measure word is added for uncountable nouns in English. For example:
For example, apple is usually countable (two apples), but it also has a non-count sense (e.g., this pie is full of apple). When discussing different types of something, a count form is available for almost any noun (e.g., This shop carries many cheeses . = "many types of cheese").
In order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are order-isomorphic.For instance, Minkowski's question-mark function produces an isomorphism (a one-to-one order-preserving correspondence) between the numerical ordering of the rational numbers and the numerical ordering of the dyadic rationals.