Question

Consider the relation on the real numbers R. a ~ b if (a−b) ∈ Z. (Z...

Consider the relation on the real numbers R. a ~ b if (a−b) ∈ Z. (Z is the whole integers.)

1) Give two real numbers that are in the same equivalence class.

2) Give two real numbers that are not in the same equivalence class.

3) Prove that this relation is an equivalence relation.

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