Given the set S, where aSb if and only if a - b [itex]\in[/itex] [itex]Z[/itex](adsbygoogle = window.adsbygoogle || []).push({});

It is asking for the equivalence class and the answer given is

S has only one equivalance class for each real number x such that 0 ≤ x < 1. the class [x] is given by {x + k : k [itex]\in[/itex] [itex]Z[/itex]}

i dun get it, since S is a set of relation where a - b is an element of Z, then there should be a lot of equivalance class for S, however, it states that S has only one equivalence class and its {x + k}

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# Equivalence classes

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