Abstract
It seems that our intuition, or at least the intuitions of 19th Century mathematicians, was that a function is naturally differentiable. It is differentiable, they felt, unless it is obviously not, perhaps because it has a sudden change of direction or because it is not even continuous, but such events would only happen at isolated points.
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The value of the floor function at x is the greatest integer less than or equal to x.
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The letter was published in volume 39 of Acta Mathematica, which Mittag-Leffler devoted to the life and work of Weierstrass in 1923, and which carried a number of historically valuable sources.
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Gray, J. (2015). The Fundamental Theorem of the Calculus. In: The Real and the Complex: A History of Analysis in the 19th Century. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23715-2_24
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DOI: https://doi.org/10.1007/978-3-319-23715-2_24
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