Ex slept with someone else soon after breakup?

My ex and I broke up for about a month after being together for a year and a half. He slept with someone else during the one month (ish) period we were broken up. Though I had expected/hoped we'd get back together, I don't think he thought we could work things out and I think he saw the breakup as final. Now he wants to get back together and though he originally lied, he came clean admitting he had slept with someone else he met on an dating app after we broke up in an effort to try to move on/get over me, but realized he couldn't get over me and that he only wanted to be with me. He apparently slept with this woman twice and hung out with her a handful of times. I didn't hookup or date anyone else during the breakup, and I really expected he wouldn't either. Should I be able to forgive him? Is the relationship irreparable now? I didn't think I would be able to forgive him if he had slept with other people after breaking up, which is why I didn't want to break up in the first place.
Ex slept with someone else soon after breakup?
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