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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.
Also much in general-language use among mathematicians: "Of course, this problem can be arbitrarily complicated". eventually In the context of limits, this is shorthand meaning for sufficiently large arguments; the relevant argument(s) are implicit in the context.
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]
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.
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 ...
In this section, the symbols that are listed are used as some sorts of punctuation marks in mathematical reasoning, or as abbreviations of natural language phrases. They are generally not used inside a formula. Some were used in classical logic for indicating the logical dependence between sentences written in plain language. Except for the ...
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language.In most scenarios a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory.