"Objections... inspired Kronecker and others to attack Weierstrass' "sequential" definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals."
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Eric Temple Bell, Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré (1937)
https://en.wikiquote.org/wiki/Karl_Weierstrass
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Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the "father of modern analysis".
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