You're taking a map from R -> R, I'm taking a sequence of discrete values. It's not the same thing. However, I was a bit fast and loose, the sequence .9, .99,

You're taking a map from R -> R, I'm taking a sequence of discrete values. It's not the same thing. However, I was a bit fast and loose, the sequence .9, .99, .999, .9999 also gets closer and closer to 2 but it doesn't converge to 2, I should have said if you have a metric || and some number X such that for any d, there exists an N such that |X -An| < d for all n > N, then the sequence A converges to X. But I wasn't trying to write a proof. https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of...