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    Continuous Map

    Alternate names

    map | mapping

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    A function f is continuous at a number a if: 1.f(a) is defined, 2.lim_(x->a) f(x) exists and 3.lim_(x->a) f(x) = f(a). If f is continuous for every number a in its domain, then f is a continuous function.

    A function f is a rule that assigns to each element x in a set D (called the domain of f) exactly one element, called f(x), in a set C (called the codomain of f).

    Details

    concepts involved | function | limit of a function | domain of a function related concepts | derivative

    concepts involved | set | domain of a function | codomain of a function related concepts | range of a function

    Associated people

    Bernard Placidus Johann Nepomuk Bolzano

    Gottfried Leibniz | Leonhard Euler

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