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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.
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
Other technical terms are words of the common language that are used in an accurate meaning that may differ slightly from their common meaning. For example, in mathematics, "or" means "one, the other or both", while, in common language, it is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called ...
Language-based learning disabilities or LBLD are "heterogeneous" neurological differences that can affect skills such as listening, reasoning, speaking, reading, writing, and math calculations. [1] It is also associated with movement, coordination, and direct attention. LBLD is not usually identified until the child reaches school age.
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.