How do I prove this a+N=N+a where a+N={a+n:n member of N} and

N+a={n+a:n member of N}

Let G=(G,+,-,0) be a group.

Let thata be member congruence(G).

Let N=[0]thata.

Then For all a member of G prove a+N=N+a

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- April 1st 2010, 10:44 AMhcourcheGroup theory problem with congruence relations
How do I prove this a+N=N+a where a+N={a+n:n member of N} and

N+a={n+a:n member of N}

Let G=(G,+,-,0) be a group.

Let thata be member congruence(G).

Let N=[0]thata.

Then For all a member of G prove a+N=N+a - April 1st 2010, 12:02 PMDrexel28