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What I believe is this. To forgive a sin is to pardon the one who has offended us, as if the offence was never committed. We allow the offender go free without anything to pay back. Our heart is pleased with him without any pain in our heart. This is manifested in the way we behave towards the person. To forget the sin is a different thing entirely. Our system is wired with memory cells which can store both interesting and painful experience. How you will know you have truly forgiven someone is that, even when you remember, you do not feel pain in your heart or hold animosity against the individual. Your mind is free towards him, and you are not eager to remind him he once sinned against him.