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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.
In the context of limits, this is shorthand for arbitrarily large arguments and its relatives; as with eventually, the intended variant is implicit. As an example, the sequence is frequently in the interval (1/2, 3/2), because there are arbitrarily large n for which the value of the sequence is in the interval.
A language L is said to be a context-free language (CFL), if there exists a CFG G, such that = (). Non-deterministic pushdown automata recognize exactly the context-free languages. Examples
A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language. Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics.
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules called a formal grammar. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings called words. [1]
The influence of context parameters on language use or discourse is usually studied in terms of language variation, style or register (see Stylistics). The basic assumption here is that language users adapt the properties of their language use (such as intonation, lexical choice, syntax, and other aspects of formulation ) to the current ...
An interpretation is an assignment of meaning to the symbols of a formal language.Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation.
The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them. For example, in a statistical linear model , it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables.