This is not even a map.
Ones gets "mapped" to,
The other is "mapped" to,
The results are clearly not the same.
Q: Let f:[0,1]->[0,1] be a function defined as follows.
Take x in [0,1] with the decimal expansion x=.x1x2x3x4x5.....
Map it to y in [0,1] such that y=.x1x3x5......
Prove that this map is continuous but nowhere differentiable in [0,1].
I need some help for this problem.
If anybody has a solution please mail me at email@example.com