I am trying to write 'functions' for them

My attempt:

A. Maybe I could write something like \(\displaystyle x = n \forall n \in \mathbb{N}\) and \(\displaystyle 0 \leq y \leq 1\). I don't know if this is a valid way to define a 'function'? Clearly if this is right then for B. the range for y could just be extended.

C. This should be something like \(\displaystyle y^2 = x\) but repeating every 1, and I'm not sure how I can do this.

Thanks in advance for your help.