Thread: Group 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

Originally Posted by hcourche

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

What is going on here? I for one can't understand what you're asking.