Similarly, the hyperreals are not the same thing as limits. Nobody ever told me: Calculus lets you work at a better level of accuracy, with a simpler model, and bring the results back to our world. 02 Apr 2019. Limits and infinitesimals. We’ll lose information if we don’t. So many math courses jump into limits, infinitesimals and Very Small Numbers (TM) without any context. The notion of zero is biased by our expectations. Note that the sequence gets closer and closer to 1, and therefore, its limit is 1. I call it Calculus Sans Limits. Well, “i” sure looks like zero when we’re on the real number line: the “real part” of i, Re(i), is indeed 0. Equivalently, the common value of the upper limit and the lower limit of a sequence: if the upper and lower limits are different, then the sequence has no limit (i.e., does not converge). Infinitesimals build the model in another dimension, and it looks perfectly accurate in ours. 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