Not sure if there's a post out there already, but how long did it take your ex to realize their loss and beg for you back?
Don't need a long story, just time (days, weeks, months, years)?
Also, was it a nasty yelling break up or a cordial calm break up?
I can guarantee you that NO HEALTHY RELATIONSHIP involves begging. If someone comes back because they were begged into it, they are retuning out of pity. Do you want someone to pity you? Indeed, there are breakups that are neither nasty nor cordial, but somewhere in between. In my case, I was shocked, and it was fairly quiet, but the tension was definitely in the air.
Show them that you don't need them and move on and then they will see the mistake they made by breaking up with you.
If you don't run in the same circles, how are they going to see that you don't need them? And, from many a dumpers viewpoint, maybe no matter what it wasn't a mistake for them to leave.