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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.
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.
Being countable implies being subcountable. In the appropriate context with Markov's principle , the converse is equivalent to the law of excluded middle , i.e. that for all proposition ϕ {\displaystyle \phi } holds ϕ ∨ ¬ ϕ {\displaystyle \phi \lor \neg \phi } .
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:
Example (4) is a statement that refers to the cat species as a whole; in other words, The cat species is common (4'); even though that there is no single individual cat that has the attribute of being common. (1') All cats are animals. (2') Most cats like fish. (3') There are some cats everywhere. (4') The cat species is common.
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"). [22]
The best known example of an uncountable set is the set of all real numbers; Cantor's diagonal argument shows that this set is uncountable. The diagonalization proof technique can also be used to show that several other sets are uncountable, such as the set of all infinite sequences of natural numbers (see: (sequence A102288 in the OEIS)), and the set of all subsets of the set ...