My crush is talking to another girl should I give up? Or should I make an effort to get to know him better?

Anonymous
When I first met my crush he had a girlfriend at the time so I would just talk to him at work. He only mentioned her once to me and he never talks about other girls. I found out from someone else that he is talking to a new girl but she doesn't think they are serious. His ex-girlfriend cheated on him and its only been like two months since they broke up. I kinda feel like she's a rebound but I'm not sure. I asked for his number and he gave it to me. Should I text to him and see where it goes? I feel like he likes me by the way he acts.
My crush is talking to another girl should I give up? Or should I make an effort to get to know him better?
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