Is it normal to forgive a cheater? Would you?

I think I can in time with the aid of prayer and discernment forgive someone for hurting me, but that forgiveness doesn't need to include reconciliation. I think the thing to do is to leave a cheater and not look back, then forgive the cheater when one feels ready so as not to be burdened with the emotional baggage. I hate the assumption that people make that forgiveness means one must take a person back.

Forgive, but don't forget. Fool me once shame on you, fool me twice shame on me.