I played a head game with my bf and found out what I didn't want to find. Is what he did considered cheating?

Ok so I know what I did was wrong, but I felt reason to do this. My boyfriend and I are long distance. we see each other any where from once a week to once a month. I was suspicious of him due to other girl drama at the beginning of our relationship. I finally decided to create an e-mail account of a pretty girl who lived in the same city. He IM her right away. He told her he was single. When asked about a supposed relationship with me he denies it that we are still dating. He also goes on to say the fake girl is prettier than me. Once again I know this is a head game, but I felt there to be a reason to do this. He tells me he loves me still and he was just having fun talking to this girl for a moment. He claims he had full intentions if blocking her and that he was being an idiot and that this was just the guy thing to do. I have ended it with him. I want to know if what he did was true betrayal. I hope to receive answers from both guys and girls. What would you all do in this situation. by the way this is a very serious 6 month relationship.