| Darboux Function |
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there exists some ''x'' with ''a'' < ''x'' < ''b'' such that ''f''(''x'') = ''z''. By the Intermediate Value Theorem , every Continuous Function is a Darboux function. Darboux's contribution was to show that there are discontinuous Darboux functions. Construction of a discontinuous Darboux function can proceed in at least two ways. One can use Transfinite Induction on Ω , or a construction involving Hamel Bases . |
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