that I know (some I do not). Some questions are a matter of opinion
in terms of what you consider natural.
- Is there a subset of [0,1] that is uncountable and has measure 0?
- Is there such a set that is natural?
- Is there a function that is continuous everywhere and differential nowhere?
- Is there such a function that is natural?
- Is there a function that has derivative 0 at almost every points of [0,1] even though it is strictly increasing?
- Is there a natural such function?
I request that all comments be NON-anonymous. (I'll tell you why when I post the answers I know on Tuesday.)