“If a is any definite number, then all numbers of the system R fall into two classes, A1 and A2, each of which contains infinitely many individuals; the first class A1 comprises all numbers a1 that are < a, the second class A2 comprises all numbers a2 that are > a; the number a itself may be assigned at pleasure to the first or second class, being respectively the greatest number of the first class or the least of the second. In every case the separation of the system R into the two classes A1, A2 is such that every number of the first class A1 is less than every number of the second class A2.”

p, 125
Stetigkeit und irrationale Zahlen (1872)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "If a is any definite number, then all numbers of the system R fall into two classes, A1 and A2, each of which contains …" by Richard Dedekind?
Richard Dedekind photo
Richard Dedekind 13
German mathematician 1831–1916

Related quotes

Oliver Wendell Holmes Jr. photo

“A second class mind, but a first class temperament.”

Oliver Wendell Holmes Jr. (1841–1935) United States Supreme Court justice

A summation of his opinion of Theodore Roosevelt, indicated in various letters, but not recorded in so succinct a form; often incorrectly stated as his opinion of Franklin D. Roosevelt, as indicated in the p. xiv–xv Introduction to The Essential Holmes (1992) http://books.google.com/books?id=HamEkfqdMcEC&pg=PR14&lpg=PR14, edited by Richard A. Posner.
Attributions

Lotfi A. Zadeh photo
Antonio Negri photo
Richard Dedekind photo
Robert Benchley photo

“In America there are two classes of travel — first class, and with children.”

Robert Benchley (1889–1945) American comedian

Source: "Kiddie-Kar Travel", Pluck and Luck (1925) http://books.google.com/books?id=ODtLAAAAIAAJ&q=%22In+America+there+are+two+classes+of+travel+first+class+and+with+children%22&pg=PA6#v=onepage; also in D.A.C. News http://www.dacnews.com/, September 1923 http://books.google.com/books?id=uLl9ULzkvikC&q=%22Kiddie+kar+travel%22&pg=PA27#v=onepage

Simon Stevin photo

“The second Definition. Number is that which expresseth the quantitie of each thing.”

Simon Stevin (1548–1620) Flemish scientist, mathematician and military engineer

Disme: the Art of Tenths, Or, Decimall Arithmetike (1608)

Martin Luther King, Jr. photo

“It is a trite yet urgently true observation that if America is to remain a first-class nation, it cannot have second-class citizens.”

Martin Luther King, Jr. (1929–1968) American clergyman, activist, and leader in the American Civil Rights Movement

1960s, The Rising Tide of Racial Consciousnes (1960)

Related topics