Equivalence relation on set r of all real numbers

Reference no: EM13130609

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

Reference no: EM13130609

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