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The English language has a number of words that denote specific or approximate quantities that are themselves not numbers. [1] Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles ...
This function typically comes before any modifiers in the NP (e.g., some very pretty wool sweaters, not *very pretty some wool sweaters [a]). The determinative function is typically obligatory in a singular, countable, common noun phrase (compare I have a new cat to *I have new cat).
Quantifiers indicate quantity. Some examples of quantifiers include: all, some, many, little, few, and no. Quantifiers only indicate a general quantity of objects, not a precise number such as twelve, dozen, first, single, or once (which are considered numerals). [5]
In some mathematical theories, a single domain of discourse fixed in advance is assumed. For example, in Zermelo–Fraenkel set theory, variables range over all sets. In this case, guarded quantifiers can be used to mimic a smaller range of quantification. Thus in the example above, to express
Many words of different parts of speech indicate number or quantity. Such words are called quantifiers. Examples are words such as every, most, least, some, etc. Numerals are distinguished from other quantifiers by the fact that they designate a specific number. [3] Examples are words such as five, ten, fifty, one hundred, etc.
Some further examples of quantities are: 1.76 litres of milk, a continuous quantity; 2πr metres, where r is the length of a radius of a circle expressed in metres (or meters), also a continuous quantity; one apple, two apples, three apples, where the number is an integer representing the count of a denumerable collection of objects (apples)
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃x" or "∃(x)" or ...
In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases . For example, the generalized quantifier every boy denotes the set of sets of which every boy is a member: { X ∣ ∀ x ( x is a boy → x ∈ X ) } {\displaystyle \{X\mid \forall x ...