Yes, some people simply never see their expartners again.. Just like that. It is the only thing that works when it is painful for one party.
I think you need to make that cut too. Even for your kids sake. And I suppose that your kids can sense that something's amiss anyway even though you say they don't know he's gone.
Draw a line, do whatever you need to do to end this (in your head and heart). Clear out his stuff, unfriend his friends on twitter and fb.. Even if they have also become your friends... When it comes down to it you have to rid yourself of everything and everyone to do with your ex.
Don't count mythological numbers in your head like PP said, and I agree, keep busy, don't hang onto the midlife crisis excuse... Your ex has left ou for another woman - do you really want him back ?
Start a new life for yourself. Change your furniture around, try and meet some new people, change your hairstyle.. Out with the old.
I have never managed to stay friends with an ex, especially when I have been dumped.
I am really sorry for this shit you are going through, have also read your other thread. Cut him out of your life or you might be in for a prolonged ending.... I am talking from experience. You need to be stronger than this!