I had this discussion in my Sunday school class months ago. We all (being several divorced people & a few married people) came to the agreement that we need to forgive like the Bible says (it actually tells us to forgive a person 70 times 7). BUT that does not mean we have to forget. Nor do we have to continue to place ourselves in the same situation over & over again & therefore having to forgive over & over again.
I was cheated on- twice. The 1st time I forgave my H & tried to work things out. He cheated on me yet again & again I forgave him & tried to work it out. Eventually I realized it wasn't working. This is when I forgave him again & divorced him. I would rather remove myself from the situation than to have to keep forgiving him for something I could essentially control on my part.
It's like the old saying "Fool me once, shame on you. Fool me twice, shame on me."
Forgiving is tricky, and it has different meanings for different people. But don't ever forget, as some others have said, because it only sets you up to be hurt again. Always remember and be on the lookout.