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Give me a function that is piecewise continuous but not piecewise smooth

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- Thread starter AlonsoMcLaren
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- #1

- 90

- 2

Give me a function that is piecewise continuous but not piecewise smooth

- #2

arildno

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- #5

pwsnafu

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jmm, the domain of of the function you wrote down is the reals minus 0. So it is irrelevant what the function is doing at the origin.

Further as micromass has noted, even if you define abs(0) = 0, the function will still be piecewise smooth. This is because you can split the domain into [itex](-\infty,0) \cup [0,\infty)[/itex], and so abs has

- #6

lavinia

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For a weird example, I was told that there is a continuous map of the sphere into the plane that is everywhere distance preserving. Such a map can not be differentiable anywhere.

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