<human>: Can you condense the text into a few key points?

I've never gone through break up before... since this is the only and the most serious relationship i have had.

It is completely my fault that i flirted with some girls online...twice
I lost my trust that i had given her, and the security i had provided to her.

It's been almost a month already. I can feel that this relationship is pretty dead... I tried to text her few times a day...either no response or only few words. I feel that she isn't even mad anymore...she just doesn't have the feeling to me anymore

this is my biggest mistake i have ever made...I didn't know what to do. I even google to see what can do i to get my ex back... and found some article quite useful and I'm try to follow those advise. 
However, they have not answered my real question. 
I recently found out that she's been with someone else couple days after we broke up. I don't think she's seriously about it tho. I still love her and don't want to give up.

My question is If i ever had this chance to get her back, but in between the break up period she probably slept with someone else, what should I think of it and what should I do? Maybe this question is dumb as fuck, but i just feel like my brain got stuck and can't think about it thoroughly
<bot>: Made mistake and broke up. She's after someone but not too serious. Should I keep trying to get her back but meanwhile I'm not sure I'm ok with that she slept with someone else.