Wikipedia:Reference desk/Archives/Mathematics/2019 September 15
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September 15
editContinuous function that is "even" at some points but "odd" at others
editLet be either the real numbers ( ) or the nonzero real numbers ( ). Then, does there exist a continuous function that is neither even nor odd but such that ? Note that since is a connected Hausdorff space, any such function with domain must have at least one x-intercept. GeoffreyT2000 (talk) 02:19, 15 September 2019 (UTC)
- Yes, and you have given yourself a hint for construction. Try to create a function which piecewise alternates being even and odd, changing over at its x-intercepts. -- ToE 04:17, 15 September 2019 (UTC)