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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 mathematics, a symbolic language is a language that uses characters or symbols to represent concepts, such as mathematical operations, expressions, and statements, and the entities or operands on which the operations are performed.
The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like:
A spoken language is a form of communication produced through articulate sounds or, in some cases, through manual gestures, as opposed to written language. Oral or vocal languages are those produced using the vocal tract, whereas sign languages are produced with the body and hands.
Reading by using phonics is often referred to as decoding words, sounding-out words or using print-to-sound relationships.Since phonics focuses on the sounds and letters within words (i.e. sublexical), [13] it is often contrasted with whole language (a word-level-up philosophy for teaching reading) and a compromise approach called balanced literacy (the attempt to combine whole language and ...
The first sense dominates in areas of mathematics and logic that deal with the formal description of languages and their meaning, such as formal language theory, mathematical logic and process algebra. [2] In informal discussions, the term often refers to the second sense, or to both. This is often the case when discussing programming languages.
The gradual disuse of Latin opened an uneasy transition period as more and more works were only accessible in local languages. Many national European languages held the potential to become a language of science within a specific research field: some scholars "took measures to learn Swedish so they could follow the work of [the Swedish chemist] Bergman and his compatriots."
A formal language can be thought of as identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems. A logical symbol is a fundamental concept in logic , tokens of which may be marks or a configuration of marks which form a particular pattern.