of Mathematics (1937; still being reprinted), Godfrey Hardy and E. M. Wright's An Introduction to the Theory of Numbers (1938; 2008 6th edition), Garrett Birkhoff and Saunders Mac Lane's A Survey of Modern Algebra (1941; 1997 5th edition), and Michael Spivak's Calculus (1967; 2008 4th edition). Since 2014, at least two books have appeared stating that Cantor's proof is constructive, and at least four have appeared stating that his proof does not construct any (or a single) transcendental. Asserting that Cantor gave a non-constructive argument without mentioning the constructive proof he published can lead to erroneous statements about the history of mathematics. In A Survey of Modern Algebra, Birkhoff and Mac Lane state: "Cantor's argument for this result [Not every real number is algebraic] was at first rejected by many mathematicians, since it did not exhibit any specific transcendental number." The proof that Cantor published produces transcendental numbers, and there appears to be no evidence that his argument was rejected. Even Leopold Kronecker, who had strict views on what is acceptable in mathematics and who could have delayed publication of Cantor's article, did not delay it. In fact, applying Cantor's construction to the sequence of real algebraic numbers produces a limiting process that Kronecker accepted—namely, it determines a number to any required degree of accuracy. The influence of Weierstrass and Kronecker on Cantor's article Historians of mathematics have discovered the following facts about Cantor's article "On a Property of the Collection of All Real Algebraic Numbers": Cantor's uncountability theorem was left out of the article he submitted. He added it during proofreading. The article's title refers to the set of real algebraic numbers. The main topic in Cantor's correspondence was the set of real numbers. The proof of Cantor's second theorem came from Dedekind. However, it omits Dedekind's explanation of why the limits a∞ and b∞ exist. Cantor restricted his first theorem to the set of real algebraic numbers. The proof he was using demonstrates the countability of the set of all algebraic numbers. To explain these facts, historians have pointed to the influence of Cantor's former professors, Karl Weierstrass and Leopold Kronecker. Cantor discussed his results with Weierstrass on December 23, 1873. Weierstrass was first amazed by the concept of countability, but then found the countability of the set of real algebraic numbers useful. Cantor did not want to publish yet, but Weierstrass felt that he must publish at