can you really forgive , if you dont forget??

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My partner cheated on me twice and asked for another chance, because of my love for her, i forgave her for the second time around. But she also wants me to forget what happened but even if how hard i tried to forget what happened, it always remain in my mind and the pain is always there everytime i think about her cheating..I totally forgave her in all the bad things she have done to me but i just cant forget that so easily. It takes years for me to forget those i think.