For forgiveness to take place, the person who did wrong and the person who was wronged each have responsibilities. The person who did wrong needs to do teshuvah (recognize their wrongdoing, feel sincere regret, resolve never to repeat the action, make amends and ask for forgiveness). And Jewish law asks the person who was wronged to open their heart and grant forgiveness (assuming that the person who did wrong did teshuvah and asked for forgiveness). Even when there is no apology and request for forgiveness, it is often better to forgive or at least to let go of grudges and resentments. Jewish law specifies when forgiveness is required, optional and forbidden. Only the victim can forgive the act of wrongdoing, so we cannot forgive offenses committed against others.
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