I've lived this one unfortunately, I was married 27 years. She had several affairs over the years. I forgave the first ones but trust never came back. I really stayed for my kids but after learnibg of the third one I decided it was time to leave. I see now I should have left after the first time, it wasn't better for the kids. I was miserable and they knew it. Once trust is destroyed it's a very hard thing ever get back. I would never recommend wasting your life messing with people that violate our trust. It's your life so no one can say what's right for you. I have since found out about a number of other affairs she had including one that lasted over 10 years. I'm sure I still don't know of them all as she never admitted anything until the evidence was overwhelming. If they haven't come out and told you things you didn't already know then they aren't being honest from my experience.

I never forgive, not because I am an atheist, forgiveness is just not in my nature, I do not understand it.

I'm sorry that this has happened to you. As a non-believer my advice to you would be to either stay or leave as you choose and to definitely be comfortable with your choice. 'Faithfulness' is a human invention, not a natural one. (And possibly a church invention - the clue is in the name.) Consider: what if monogamy is unnatural for a person? We realise now that LGBQTIA is not unnatural - in fact it's biological, so what if there are some people who just aren't monogamous? To love a person conditionally upon it being equally reciprocated... might not be true love. I have known gay people who have had long term relationships while being deeply in love with each other but struggling with monogamy. Ask a scientist what love is - it's complicated, and it's also simple. It exists to make sure the human race keeps breeding. It does so by hijacking your brain chemically, but then the brain recovers from that addiction. Love then has to change into something else.
Ahhh, dammit. What the hell do I know. I know I love my wife completely, but she says she doesn't believe me because I don't show it, and she doesn't feel it.

That pretty much describes my life as of last October. Coping is hard, but it's not like I have a choice. Being a believer or non-believer of god(s) doesn't enter into the equation at any point. I wasn't given any choices about how things went down. And no, I don't forgive him and I don't feel guilty about not forgiving him.

No relationship based on dishonesty can last. How can you trust someone who you know has deceived you for decades? The best predictor of future behavior is past behavior. It's over.

What does non-believing has got to do with it?

The most important one to 'forgive' is yourself for either having misjudged the other or for really knowing on a deeper level and not allowing yourself to confront it out of some illusion of probable loss by doing so.

Trust is only half trust as it applies to the other. The other half is self-trust in your own perceptions and judgments. Only we can be responsible for that half. It is 'we' that will be with us for the rest of life and therefore more important to make peace at home and learn from it.

The other is irrelevant after separation.

Faith doesn't have a monopoly on forgiveness. I think forgiveness isn't something you grant, or bestow, as though granting forgiveness gives you a new power over someone. I don't know your marriage, but I would hope that in a similar situation, when I'm with someone I truly love, I would be able to find it on my heart to forgive.

I do not forgive for major acts of betrayal. Fuck forgiveness, they are not entitled to it.

NO! I'm gone. Being a nonbeliever has nothing to do with trust.

Personally, I'd kick their cheating ass to the curb. But I'd Also forgive them, which to me is just letting go of the hurt, because that isn't for them, it's for me. But that bridge would be gone. Nuked from orbit, earth scorched and salted for good measure.

I felt lost... like I'd lost my best friend (and I had). I forgave him, though, as he didn't deliberately try to hurt me. His own issues caused his own downfall. (This is in hindsight, of course - I was devastated at the time.) Divorced after that, regardless.

Forgive but don't forget.

I would feel betrayed. I'd have to divorce them.

Cheats are selfish children.

Sex is no big deal ! Either you handle it or you don't ?   you choose !

However you choose.

Was it a one time occurrence, or ongoing? If one time, have they convinced you that it won't happen again? If ongoing, it will happen again and you would be foolish to forgive, in my opinion. It's hard to divorce and start over, but sometimes worth it.

I'm sorry that you have to face this.

Unfaithful-using the word as not being honest