感謝核實與點評。修改了f~g

來源: 2024-09-16 14:28:47 [博客] [舊帖] [給我悄悄話] 本文已被閱讀:

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.

證明: 

1. 自反性: 顯然, pRp 

2. 對稱性: pRq=qRp 

3. 傳遞性: pRq and qRt then pRt