Pls inform me about equivalence class...i am not understanding it

Dear student.
[0]={0,±2,±4,±6}
We have
 R={(a,b):2 divides a−b}
For any a∈Z
[a]={x:(x,a)∈R}={x:2 divides x−a}
[0]={x∈Z:2 divides x−0}={x∈Z:2 divides x}={0,±2,±4,±6,...}
Regards

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