Il logo di batmath
previous page | next page


A function that is not continuous at a point c of its domain is called discontinuous at c. Usually this concept of discontinuity is used also in a larger sense:  if a point c is an accumulation point of the domain that does not belong to the domain, then the function is called discontinuous at c. For example the function f(x)=lnx is called discontinuous at zero. But pay attention because, as zero does not belong to the domain, it makes no sense to ask whether the functions is continuous or not at zero. So, strictly speaking, the function is neither continuous not discontinuous at zero: the word discontinuous is used here in a somewhat improper sense.

A function may be discontinuous at a point c (that belongs to the domain or is an accumulation point for the domain) for one of the following reasons:


previous page | next page
first published on march 26 2002 - last updated on september 01 2003