Forgiving her for cheating?
Yes, of course.
She is a human being and humans can and will fuck up sometime in their lives.
Because in our DNA there is nothing saying we are monogamous creatures.
Actually, we are build to fuck as many times as we can with as many people we can.
Since the beginning of times.
So, why been surprised when people go to bed with other people?
That is what our DNA tells us to do.
Social convention tells us that we must be monogamous and not be fooling around.
Yeah, a social convention, nothing else.
Problem is this is against our human nature.
So, if your significant other went to bed with someone, should you ignore it and do nothing about it?
No, talk about it, and if the desire to keeping it going is there, but your SO is willing to continue to live with you, just accept it and move on.
This is quite common and is called polyamorous way of life.
There are lots of people here in Quora who does exactly that and you will see they live quite an interesting life.
All the best