Jacobs, Jan wrote:
> 1. Do functions f exists on R -> R that are continuous?

Here is an idea as to how to approach this.

Let g:[0,1]->[0,1] be an arbitrary continuous function with g(0)=1,
g(1)=1/2.

Define f=g on [0,1].  Now extend f to (1,2] by using

f(1+x)=1+x - f f(x)=1+x - f g(x)=1+ x - g g(x),

since x is in (0,1].  Keep going.

Best iwhses,

John


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