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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]
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.
Denotation. In linguistics and philosophy, [1] the denotation of a word or expression is its strictly literal meaning. For instance, the English word "warm" denotes the property of having high temperature. Denotation is contrasted with other aspects of meaning including connotation. For instance, the word "warm" may evoke calmness, coziness, or ...
C. calculus. (From Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus) [8] is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. Cavalieri's principle.
Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous arguments or precise ideas. Much of this is common English, but with a specific non-obvious meaning when used in a mathematical sense. Some phrases, like "in general", appear below in more than one section.
a. a city named Buffalo. This is used as a noun adjunct in the sentence; n. the noun buffalo, an animal, in the plural (equivalent to "buffaloes" or "buffalos"), in order to avoid articles. v. the verb "buffalo" meaning to outwit, confuse, deceive, intimidate, or baffle. The sentence is syntactically ambiguous; one possible parse (marking each ...
The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom".
In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean -valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed ...