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On an unrelated note, Batman's dog is a mutant or something, because I'm watching Batman Beyond(the movie, not the show), and the original Batman is really old, like 30 or more years into the future, and he has the same dog.
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I'm pretty sure he didn't get Ace until sometime between JLU and Batman Beyond, so it's not that weird. He probably got it 5-10 years ago to keep him company, seeing as nobody ever talks to him anymore. That's my guess, at least.
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But I'm not sure if you're a Batman fan.
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I am a huge Bruce Timm DC Universe fan. I have been since Batman: The Animated Series, and I probably always will be.