Consider [x] denote integer part of x, i.e largest integer less than or equal to x. Let relation \approx defined on R by: x \approx y if x-[x] = y-[y]
i) Illustrate that approx is the equivalence relation.
ii) Determine its equivalence classes?
iii) Illustrate that function: \Phi:(R X R/\approx) \rightarrow [0,1) \Phi(x) = x-[x] is a 1-1 correspondence. Here x denotes equivalence class of x under \approx. Ensure to first prove that \Phi is well-defined.