“If there is some determinate succession of defined whole real numbers, among which there exists no greatest, on the basis of this second principle of generation a new number is obtained which is regarded as the limit of those numbers, i. e. is defined as the next greater number than all of them.”
From Kant to Hilbert (1996)
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Georg Cantor 27
mathematician, inventor of set theory 1845–1918Related quotes

Source: A Discourse of Combinations, Alterations, and Aliquot Parts (1685), Ch.I Of the variety of Elections, or Choice, in taking or leaving One or more, out of a certain Number of things proposed.

“I am for those means which will give the greatest good to the greatest number.”
Speech to Germans at Cincinnati, Ohio (February 12, 1861); published in The Collected Works of Abraham Lincoln (1953) by Roy P. Basler, vol. 4, p. 202<!-- New Brunswick, N.J.: Rutgers University Press -->
The phrase "I am for those means which will give the greatest good to the greatest number." is allusion to British jurist, philosopher, and legal and social reformer Jeremy Bentham who wrote in his "Extracts from Bentham's Commonplace Book", in Collected Works, x, p. 142: "Priestley was the first (unless it was Beccaria) who taught my lips to pronounce this sacred truth — that the greatest happiness of the greatest number is the foundation of morals and legislation."
1860s
Context: I agree with you, Mr. Chairman, that the working men are the basis of all governments, for the plain reason that they are the most numerous, and as you added that those were the sentiments of the gentlemen present, representing not only the working class, but citizens of other callings than those of the mechanic, I am happy to concur with you in these sentiments, not only of the native born citizens, but also of the Germans and foreigners from other countries. Mr. Chairman, I hold that while man exists, it is his duty to improve not only his own condition, but to assist in ameliorating mankind; and therefore, without entering upon the details of the question, I will simply say, that I am for those means which will give the greatest good to the greatest number.

“Fascism is not defined by the number of its victims, but by the way it kills them.”
"On the Execution of Julius and Ethel Rosenberg," Libération (22 June 1953)
Source: Mathematics and the Physical World (1959), p. 51.

Source: The Age of Revolution (1962), Chapter 13, Ideology: Secular