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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 ...
The determinative function is typically obligatory in a singular, countable, common noun phrase (compare I have a new cat to *I have new cat). Semantically , determiners are usually definite or indefinite (e.g., the cat versus a cat ), [ 4 ] and they often agree with the number of the head noun (e.g., a new cat but not * many new cat ).
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.
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.
a; a few; a little; all; an; another; any; anybody; anyone; anything; anywhere; both; certain (also adjective) each; either; enough; every; everybody; everyone ...
Warriner's English Grammar and Composition is a series of textbooks on English grammar and composition by John E. Warriner, consisting initially of six books targeted at grades 6 through 12, in numerous editions, with publication beginning in 1946 and a 7th book added in 1959. [1]
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 } .
In order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are order-isomorphic.For instance, Minkowski's question-mark function produces an isomorphism (a one-to-one order-preserving correspondence) between the numerical ordering of the rational numbers and the numerical ordering of the dyadic rationals.
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