The nearest integer function is the name of the function that we associate with “rounding” to the nearest integer. For a given real number x , the nearest integer function is usually denoted by [ ] ....

The nearest integer function is the name of the function that we associate with “rounding” to the nearest
integer. For a given real number x , the nearest integer function is usually denoted by [ ] . Do not confuse
this with the notation for “equivalence class” which also uses brackets. Here are some examples:
[2.791] = 3 , [0.257] = 0 , [5/3] = 2 , [7.5] = 8 , [–5.49] = –5 . (Notice, it is convention to round something like
7.5 up to 8, even though it is exactly in the middle of 7 and 8).
Define a relation R on the real numbers as follows: x R y if and only if [x – y] = 0. Is R an equivalence
relation? Prove or disprove