At this point, even if it was your ex who broke up with you, you don’t want to give them all the power.
You don’t want to be the one who is always available for them. Acting like your life is over without your ex will only lose their respect for you.
This is because if you tell someone to don’t do something, then you can rest assured that is exactly what they will do.
In fact, if you do so they will go to the extent of prolonging their rebound relationship just to prove you wrong.
So if your ex is seeing someone else, all you have to do is just be cool about it. Sometimes, they start seeing someone else just to rub in your face that they are moving on.