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One can also speak of "almost all" integers having a property to mean "all except finitely many", despite the integers not admitting a measure for which this agrees with the previous usage. For example, "almost all prime numbers are odd". There is a more complicated meaning for integers as well, discussed in the main article.
In mathematics, for a function :, the image of an input value is the single output value produced by when passed .The preimage of an output value is the set of input values that produce .
Pre-algebra is a common name for a course taught in middle school mathematics in the United States, usually taught in the 6th, 7th, 8th, or 9th grade. [1] The main objective of it is to prepare students for the study of algebra. Usually, Algebra I is taught in the 8th or 9th grade. [2]
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering.
Lexicalization may be simple, for example borrowing a word from another language, or more involved, as in calque or loan translation, wherein a foreign phrase is translated literally, as in marché aux puces, or in English, flea market. Other mechanisms include compounding, abbreviation, and blending. [2]
Lexical tokenization is the conversion of a raw text into (semantically or syntactically) meaningful lexical tokens, belonging to categories defined by a "lexer" program, such as identifiers, operators, grouping symbols, and data types. The resulting tokens are then passed on to some other form of processing.
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