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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.
Count nouns or countable nouns are common nouns that can take a plural, can combine with numerals or counting quantifiers (e.g., one, two, several, every, most), and can take an indefinite article such as a or an (in languages that have such articles). Examples of count nouns are chair, nose, and occasion.
A grammatical distinction is often made between count (countable) nouns such as clock and city, and non-count (uncountable) nouns such as milk and decor. [5] Some nouns can function both as countable and as uncountable such as "wine" in This is a good wine. Countable nouns generally have singular and plural forms. [4]
In Kiowa, by default, Class I nouns are singular-dual, Class II nouns are plural (two or more), Class III nouns are dual, and Class IV nouns are mass nouns with no number. The inverse number marker changes the noun to whatever number(s) the unmarked noun isn't, such as changing Class III nouns from dual to nondual. [ 277 ]
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. [a] Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time ...
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 ...
A countable non-standard model of arithmetic satisfying the Peano Arithmetic (that is, the first-order Peano axioms) was developed by Skolem in 1933. The hypernatural numbers are an uncountable model that can be constructed from the ordinary natural numbers via the ultrapower construction.
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