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An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
A technical definition is a definition in technical communication describing or explaining technical terminology. Technical definitions are used to introduce the vocabulary which makes communication in a particular field succinct and unambiguous. For example, the iliac crest from medical terminology is the top ridge of the hip bone (see ).
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied ...
Under longitudinal research methods, the reduction in the research sample will bias the remaining smaller sample. [ citation needed ] Practice effect is also one of the problems: longitudinal studies tend to be influenced because subjects repeat the same procedure many times (potentially introducing autocorrelation ), and this may cause their ...
A definition states the meaning of a word using other words. This is sometimes challenging. Common dictionaries contain lexical descriptive definitions, but there are various types of definition – all with different purposes and focuses. A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).
and what we obtain is an extension by definitions ′ of . Then in T ′ {\displaystyle T'} we can prove that for every x , there exists a unique y such that x × y = y × x = e . Consequently, the first-order theory T ″ {\displaystyle T''} obtained from T ′ {\displaystyle T'} by adding a unary function symbol f {\displaystyle f} and the axiom
It does this through the research and analysis of terms in context for the purpose of documenting and promoting consistent usage. Terminology can be limited to one or more languages (for example, "multilingual terminology" and "bilingual terminology"), or may have an interdisciplinarity focus on the use of terms in different fields.
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function.Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation which initially defined the function becomes divergent.