- #1

- 90

- 2

## Main Question or Discussion Point

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

- Thread starter AlonsoMcLaren
- Start date

- #1

- 90

- 2

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

- #2

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 9,970

- 131

- #3

- 26

- 0

- #4

- #5

pwsnafu

Science Advisor

- 1,080

- 85

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

Science Advisor

Gold Member

- 3,170

- 575

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.

- Replies
- 1

- Views
- 2K

- Replies
- 3

- Views
- 4K

- Replies
- 4

- Views
- 3K

- Replies
- 3

- Views
- 668

- Replies
- 1

- Views
- 2K

- Replies
- 1

- Views
- 4K

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 7

- Views
- 2K

- Replies
- 5

- Views
- 6K