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Reference.org
Conway's base 13 function
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<p>Conway's base 13 function is a function created by British <a href="/facts/Mathematician/eaFSR8Fx">mathematician</a> <a href="/facts/John_H._Conway/g3PA1zoK">John H. Conway</a> as a counterexample to the <a href="/facts/Converse_(logic)/VhlUrxxx">converse</a> of the <a href="/facts/Intermediate_value_theorem/SaFdYE7W">intermediate value theorem</a>. In other words, it is a function that satisfies a particular <a href="/facts/Darboux_function/uYXRzISn">intermediate-value property</a> — on any interval ( a , b ) {\displaystyle (a,b)} , the function f {\displaystyle f} takes every value between f ( a ) {\displaystyle f(a)} and f ( b ) {\displaystyle f(b)} — but is not <a href="/facts/Continuous_function/sKbl02pB">continuous</a>. </p>