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The reasons for not distinguish $f$ from $f(x)$ are historical. For roughly 250 years, from the first use of "function" in mathematics (by Leibniz ~1680) until ~1930, the official (and only) definition of the word was: A quantity $y$ is called a function of $x$, if its value is uniquely determined as soon as $x$ assumes a value. Look into any book from that ...


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I think you should consider that for most calculus students, they will have a limited exposure to e-d and then move on to massive amounts of other calculations. And that will serve the vast amount of physicists, chemists, engineers, geologists, etc. just fine. Even from a TIME usage perspective, going deeper and more intuitive into e-d may be a waste of ...


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