Discontinuities of monotone functions

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In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> field of <a href="/facts/Mathematical_analysis/XXeR26Ih">analysis</a>, a well-known theorem describes the set of <a href="/facts/Discontinuity_(mathematics)/TGLMsQom">discontinuities</a> of a <a href="/facts/Monotonic_function/MjQK0YL2">monotone</a> <a href="/facts/Real-valued_function/jetqlJpK">real-valued function</a> of a real variable; all discontinuities of such a (monotone) function are necessarily <a href="/facts/Jump_discontinuity/TGLMsQom">jump discontinuities</a> and there are at most <a href="/facts/Countable_set/Wj4DmWPv">countably many</a> of them.
</p><p>Usually, this theorem appears in literature without a name. It is called Froda's theorem in some recent works; in his 1929 dissertation, <a href="/facts/Alexandru_Froda/z9hFC9Np">Alexandru Froda</a> stated that the result was previously well-known and had provided his own elementary proof for the sake of convenience. Prior work on discontinuities had already been discussed in the 1875 memoir of the French mathematician <a href="/facts/Jean_Gaston_Darboux/evh2nMHN">Jean Gaston Darboux</a>.
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Discontinuities of monotone functions open-in-new

Discontinuities of monotone functions