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The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language (for example English) using technical terms and grammatical conventions that are peculiar to mathematical discourse (see Mathematical jargon), supplemented by a highly specialized symbolic notation for mathematical formulas. Like natural languages in general, discourse using the language of mathematics can employ a scala of registers. Research articles in academic journals use a more formal tone than oral exchanges over a scribbled-upon napkin in the university cafeteria. ==What is a language?== Here are some definitions of language: * ''a systematic means of communicating by the use of sounds or conventional symbols'' * ''a system of words used in a particular discipline'' * ''a system of abstract codes which represent antecedent events and concepts'' 〔Syntax: An Introduction, Volume 1 Talmy GivónJohn Benjamins Publishing, 2001〕 * ''the code we all use to express ourselves and communicate to others'' Speech & Language Therapy Glossary of Terms] * ''a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements'' Noam Chomsky. These definitions describe language in terms of the following components: * A vocabulary of symbols or words * A grammar consisting of rules of how these symbols may be used * A 'syntax' or propositional structure, which places the symbols in linear structures. * A 'Discourse' or 'narrative,' consisting of strings of syntactic propositions 〔Syntax: An Introduction, Volume 1 Talmy Givón John Benjamins Publishing, 2001〕 * A community of people who use and understand these symbols * A range of meanings that can be communicated with these symbols Each of these components is also found in the language of mathematics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「language of mathematics」の詳細全文を読む スポンサード リンク
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