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For instance, many nouns in English denote concrete entities, they are pluralized with the suffix -s, and they occur as subjects and objects in clauses. Many verbs denote actions or states, they are conjugated with agreement suffixes (e.g. -s of the third person singular in English), and in English they tend to show up in medial positions of ...
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
In English, prototypical nouns are common nouns or proper nouns that can occur with determiners, articles and attributive adjectives, and can function as the head of a noun phrase. According to traditional and popular classification, pronouns are distinct from nouns, but in much modern theory they are considered a subclass of nouns. [ 2 ]
In mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets (or sometimes to another category). This functor makes it possible to think of the objects of the category as sets with additional structure , and of its morphisms as structure-preserving functions.
The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc.) with concision, precision and unambiguity.
Below are examples of all the properties of count nouns holding for the count noun chair, but not for the mass noun furniture. Occurrence in plural. There is a chair in the room. (correct) There are chairs in the room. (correct) There is chair in the room. (incorrect) There is a furniture in the room. (incorrect) There are furnitures in the ...
In English, these higher words are hundred 10 2, thousand 10 3, million 10 6, and higher powers of a thousand (short scale) or of a million (long scale—see names of large numbers). These words cannot modify a noun without being preceded by an article or numeral (*hundred dogs played in the park), and so are nouns.
[10] [11] The count and non-count distinction also affects what other determiners can occur with the nouns: singular count nouns can occur with a but not some (e.g., a chair but not usually *some chair) while non-count nouns can occur with some but not a (e.g., some furniture but not *a furniture). [10] Many common nouns have both count and non ...