In mathematics, Froda's theorem, named after Alexandru Froda, describes the set of discontinuities of a (monotone) real-valued function of a real variable. Usually, this theorem appears in literature without Froda's name being mentioned. However, this result was first proven by A. Froda in 1929.One can prove that all points of discontinuity of a monotone real-valued function defined on an interval are either removable or jump discontinuities and hence, by our definition, of the first kind. With this remark Froda's theorem takes the more stronger form: Let f be a function defined on an interval I. Then the set of discontinuities of the first kind is at most countable.

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