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Auxiliary verb. An auxiliary verb ( abbreviated aux) is a verb that adds functional or grammatical meaning to the clause in which it occurs, so as to express tense, aspect, modality, voice, emphasis, etc. Auxiliary verbs usually accompany an infinitive verb or a participle, which respectively provide the main semantic content of the clause. [ 1 ...
projection. A projection is, roughly, a map from some space or object to another that omits some information on the object or space. For example, R 2 → R , ( x , y ) ↦ x {\displaystyle \mathbb {R} ^ {2}\to \mathbb {R} , (x,y)\mapsto x} is a projection and its restriction to a graph of a function, say, is also a projection.
Language of mathematics. 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.
Map (mathematics) A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [ 1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.
And/or is an English grammatical conjunction used to indicate that one or more (or even all) of the cases it connects may occur. It is used as an inclusive or (as in logic and mathematics), because saying "or" in spoken language (or writing "or") might be inclusive or exclusive . The construction has been used in official, legal and business ...
There are sentences in English in which a full verb is later 'picked up' by an auxiliary. The position is very similar to that of a noun being 'picked up' by a pronoun. [. . .] If the initial sentence, which contains the main verb, is not heard, all the remainder is unintelligible; it is, in fact, truly in code. The following example is from Firth:
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