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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: e.g., two dozen or more than a score. Scientific non-numerical quantities are represented as SI units.
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]
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).
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.
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 ...
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", or "for any". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain.
For example, one can write the meaning of sleeps as the following lambda expression, which is a function from an individual x to the proposition that x sleeps. λ x . s l e e p ′ ( x ) {\displaystyle \lambda x.\mathrm {sleep} '(x)} Such lambda terms are functions whose domain is what precedes the period, and whose range are the type of thing ...