I personally have been cheated on, and if you are or have been in the similar situation then you know it isn't a fun thing to go through. As to whether you should split should depend on the relationship. Everybody makes mistakes, right? There hasn't been a single human to make perfect decisions all the time. I think that if you truly believe that they are sorry and that it was just a poor decision made, and you really believe that they won't do it again, then maybe it won't hurt to keep going. It's going to be broken, but if the relationship is worth fixing to you, then do it. But if you have that gut feeling that it wasn't just a mistake, or that they aren't truly sorry, then don't fool yourself into staying. Fool me once, shame on you, fool me twice, shame on me. Can't get fooled again, right?