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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.
The things could be countable objects such as individual items available as units for sale, or an uncountable material. Even though the word "sample" implies a smaller quantity taken from a larger amount, sometimes full biological or mineralogical specimens are called samples if they are taken for analysis, testing, or investigation like other ...
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.
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 ...
Classifiers play a similar role to measure words, except that measure words denote a particular quantity of something (a drop, a cupful, a pint, etc.), rather than the inherent countable units associated with a count noun. Classifiers are used with count nouns; measure words can be used with mass nouns (e.g. "two pints of mud"), and can also be ...
One of the earliest results in set theory, published by Cantor in 1874, was the existence of different sizes, or cardinalities, of infinite sets. [2] An infinite set is called countable if there is a function that gives a one-to-one correspondence between and the natural numbers, and is uncountable if there is no such correspondence function.
One may fail to effectively count the subcountable set if one fails to map the counting numbers into the indexing set , for this reason. 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 ...
Any countable product of a second-countable space is second-countable, although uncountable products need not be. The topology of a second-countable T 1 space has cardinality less than or equal to c (the cardinality of the continuum). Any base for a second-countable space has a countable subfamily which is still a base.