Property of a function that is not continuous in a given interval of its domain.

If we consider an interval [m, n] of the domain of a function f of the real variable x and a value a of this interval, we say that the function f is discontinuous in this interval if f(a) is not defined or if \(\lim\limits_{x \rightarrow  a} f(x) ≠ f(a)\).

These two cases are illustrated in the examples below.


  • In the graph on the left, f(a) is not defined.
  • In the graph on the right, \(\lim\limits_{x \rightarrow  a} f(x) ≠ f(a)\).

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