Thread: Suitable function H(H(x))=H(x)

Hi just a question from the book I'm a bit puzzled with, probably fairly basic but I am very tired and can't make any sense of it :/

Find a suitable function such that , and

Hint: Don't try to solve for , the further conditions are to guide you to a suitable

I understand how they go together as in:





But I'm not sure of the form the function will take??

Thank you!

The important values of are the ones where . For such an , if is such that then clearly . Think along the lines of partitioning the reals.