感谢核实与点评。修改了f~g

S={single valued functions}

For a given g(x), if both p(x) and q(x) single valued and satisfying p(p(x))=g(x) and q(q(x))= g(x)

then pRq is an equivalent relation p~q and all such functions form an equivalent class.

证明： 

1. 自反性： 显然， pRp 

2. 对称性： pRq=qRp 

3. 传递性： pRq and qRt then pRt