Definitions
A definition is a semantic statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what the mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed.
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