Definition: fractionalpart[x] takes all digits to the right of the decimal point and drops the others. e.g. fractionalpart[123.456] = .456
Define a relation R on R(set of all reals) if fractionalpart[x] =fractionalpart[y].
I understand how to test if this is an equivalence relation (reflexive, symmetric, and transitive) but, how can I find the equivalence classes?
Is it just the set of all real numbers that have the same numbers to the right of the decimal point?