First of all, the phrase “forgive and forget” is not in the Bible. (And I couldn't find the phrase "sea of forgetfulness" either.) However, the Bible makes it quite clear that we should forgive others. “Bear with each other and forgive whatever grievances you may have against one another. Forgive as the Lord forgave you” (Colossians 3:13).

The Bible speaks of forgiveness in terms of removing the barrier that sin creates so that a relationship can be restored. Another way to define forgiveness is treating someone as though they never wronged you. That may be easy to understand, but it’s hard to do.

God is our model. There are many different images that the Bible uses to describe God’s forgiveness. Sometimes the Bible speaks of sin being sent far away. “As far as the east is from the west, so far has he removed our transgressions from us (Psalm 103:12). Other times, the Bible speaks of our sins being covered up or blotted out (Psalm 51:9). Sometimes forgiveness is pictured as a process of washing and cleansing (Psalm 51:7). Sin is also pictured as a debt or penalty, so forgiveness is when that debt is paid for or canceled. “Forgive us our debts, as we also have forgiven our debtors” (Matthew 6:12).

When God forgives, it means that he doesn’t hold our sins against us anymore. “God was reconciling the world to himself in Christ, not counting men's sins against them” (2 Corinthians 5:19). “No longer will a man teach his neighbor, or a man his brother, saying, 'Know the LORD,' because they will all know me, from the least of them to the greatest,’ declares the LORD. ‘For I will forgive their wickedness and will remember their sins no more’” (Jeremiah 31:34). The reason for all this is so that we might be reconciled in our relationship with God. Likewise, God wants us to be reconciled to other people. The Bible also makes it clear that we should forgive others as God has forgiven us. So what about forgetting?

Though we humans forget things, it is impossible to willfully forget something. The more you think about forgetting it, the more you will remember it! But it is possible to not hold it against someone anymore. This is why the Bible says, “Love keeps no record of wrongs” (I Corinthians 13:5). To forgive means that we act as though it is forgotten. “Be kind and compassionate to one another, forgiving each other, just as in Christ God forgave you” (Ephesians 4:32).

The Bible never tells us to literally forget sin. God can't literally "forget" either or he would cease to be omniscient. God still knows what happened, but he “forgets” our sin in the sense that he treats us as though the event never occurred. Is that how you and I forgive others?