Assignment:
Show that == (where == is the equivalence relation defined below) is an equivalence on A, and find a (well-defined) bijection %: A== -> B, where
(a) A = R (the set of all real numbers)
(b) B={x: x is an element of R and 0 <= x < 1}
(c) for real numbers x and y, "x==y" (x is equivalent to y) if and only if x - y is an element of Z (the set of all integers)
(d) "A==" denotes the set of all equivalence classes
Provide complete and step by step solution for the question and show calculations and use formulas.