Darboux Function Article Index for
Darboux
Website Links For
Function
 

Information About

Darboux Function




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 .