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**MattMan** It takes a bit of intuition to choose things like that. Sometimes, similar to what happened to you, you can just tell what epsilon you need. But sometimes it's not as obvious. For me, I'll sometime leave my choice of epsilon blank on my paper and continue working out the proof as if I hadn't until I get to the important usage of epsilon and see what I need there to complete the proof, and go back and fill it in. Also sometimes you might pick the wrong epsilon, but that's okay, you just go back and adjust it till it works out.