Virtual Museum of Art | Virtual Museum of History | Virtual Public Library | Virtual Science Center | Virtual Museum of Natural History | Virtual War Museum
   You are in: Virtual Public Library >> Hall of Famous Authors >> Georg Cantor





American’s Four United Republics: Discovery-Based Curriculum

For More Information go to America's Four United Republics Curriculum


 


Georg Cantor

1845-1918

Russian-born German mathematician best known as the creator of set theory

Georg Ferdinand Ludwig Philipp Cantor (St. Petersburg , 3 March 1845 - Halle , 6 January 1918) was a mathematician German, father of modern set theory . Cantor's set theory has expanded to include within it the concept of transfinite numbers , cardinal numbers and ordinal.

Cantor was born in St. Petersburg, son of Georg Cantor Woldemar, a stock trader Danish , and Marie Anna Böhm, a musician born in Russia, but of Austrian origin. In 1856 due to the state of health of the father, the family moved to Germany and Georg continued his education at German schools, first in Darmstadt, then in Switzerland ETH Zurich, finally earning his doctorate at the ' University of Berlin in 1867 with a thesis on the theory of numbers : De aequationibus Secundi gradus indeterminatis.

Cantor acknowledged that the infinite sets can have different cardinalities, separated the sets in countable and uncountable more than and proved that the set of all rational numbers Q is countable while the set of all real numbers R is more than countable, demonstrating so that there are at least two orders of infinity. He also invented the symbol that is used today to indicate the actual numbers. The method which he used to conduct his demonstration is known as the method of the diagonal Cantor. Later, he tried in vain to prove the ' continuum hypothesis . Cantor formulated a very important principle for the definition of real numbers, called the principle of localization , which is fundamental in order to operate on the above number field.

During the second half of his life he suffered from bouts of depression , which seriously compromised his ability as a mathematician and forced him to repeated hospitalizations. He began to read texts of literature and religion, in which he developed his concept of ' infinite absolute who identified with God . He wrote:

"The actual infinity comes in three contexts: first when it is realized in a more complete form, in essence mystical completely independent in God , which I call Absolute Infinite or simply Absolute; secondly when making in the contingent world, created, third when the mind grasps it in abstracto as a magnitude, number, or a type of mathematical order. "

Impoveritosi during the First World War , died in Halle where he was hospitalized in a psychiatric hospital. Leopold Kronecker judged his findings "meaningless".

A Cantor has been named the Cantor crater on the Moon .

Cantor gave rise to the theory of sets ( 1874 - 1884 ) was the first to understand that infinite sets can have different sizes: first showed that given any set , there is the set of all possible subsets , called the ' power set of . Then demonstrated that the power set of an infinite set has a magnitude greater than the magnitude of the same (this fact is now known by the name of theorem Cantor ). So there is an infinite hierarchy of sizes of infinite sets, from which arise the numbers cardinal and ordinal transfinite, and their peculiar arithmetic. To denote the cardinal numbers used the letter of ' Hebrew alphabet aleph with a natural number as an index ( Alef zero), for the ordinals used the letter of ' greek alphabet omega.

The innovative Cantorian theory, opposed during the life of its creator, has been fully accepted by modern mathematicians, who recognized in the theory of transfinite sets one paradigm shift of the first magnitude.

Works

Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Numbers . Journal für die reine und Mathematik angewandte . 1874. (First written on set theory).
Über die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen , in: Mathematische Annalen 5 (1872) 123-132.
Über die verschiedenen Standpunkte in Bezug auf das aktuale Unendliche , 1886.
Über eine der elementary Frage Mannigfaltigkeitslehre , 1890/91.
Georg Cantor: Beiträge zur Begründung der transfiniten Mengenlehre (1. Artikel), in: Mathematische Annalen 46 (1895), S. 481-512.
Georg Cantor: Beiträge zur Begründung der transfiniten Mengenlehre (2. Artikel), in: Mathematische Annalen 49 (1897), S. 207-246.
Georg Cantor: Gesammelte Abhandlungen Mathematischen und philosophischen Inhalts. Hrsg. st. E. Zermelo. Berlin: Springer, 1932. (Reprint: Springer, 1980.)
Georg Cantor: Briefe. Hrsg. st. H. Meschkowski. Berlin: Springer 1991.


Start your search on Georg Cantor.


America's Four United Republics Exhibit - Click Here


Unauthorized Site: This site and its contents are not affiliated, connected, associated with or authorized by the individual, family, friends, or trademarked entities utilizing any part or the subject's entire name. Any official or affiliated sites that are related to this subject will be hyper linked below upon submission and Evisum, Inc. review.

Research Links

  • Library of Congress
  • Carnegie Library
  • London Public Library

    Copyright© 2000 by Evisum Inc.TM. All rights reserved.
    Evisum Inc.TM Privacy Policy

  • Search:

    About Us

     

     

    Image Use

    Please join us in our mission to incorporate America's Four United Republics discovery-based curriculum into the classroom of every primary and secondary school in the United States of America by July 2, 2026, the nation’s 250th birthday. , the United States of America: We The People Click Here

     

    Childhood & Family

    Click Here

     

    Historic Documents

    Articles of Association

    Articles of Confederation 1775

    Articles of Confederation

    Article the First

    Coin Act

    Declaration of Independence

    Declaration of Independence

    Emancipation Proclamation

    Gettysburg Address

    Monroe Doctrine

    Northwest Ordinance

    No Taxation Without Representation

    Thanksgiving Proclamations

    Mayflower Compact

    Treaty of Paris 1763

    Treaty of Paris 1783

    Treaty of Versailles

    United Nations Charter

    United States In Congress Assembled

    US Bill of Rights

    United States Constitution

    US Continental Congress

    US Constitution of 1777

    US Constitution of 1787

    Virginia Declaration of Rights

     

    Historic Events

    Battle of New Orleans

    Battle of Yorktown

    Cabinet Room

    Civil Rights Movement

    Federalist Papers

    Fort Duquesne

    Fort Necessity

    Fort Pitt

    French and Indian War

    Jumonville Glen

    Manhattan Project

    Stamp Act Congress

    Underground Railroad

    US Hospitality

    US Presidency

    Vietnam War

    War of 1812

    West Virginia Statehood

    Woman Suffrage

    World War I

    World War II

     

    Is it Real?



    Declaration of
    Independence

    Digital Authentication
    Click Here

     

    America’s Four Republics
    The More or Less United States

     
    Continental Congress
    U.C. Presidents

    Peyton Randolph

    Henry Middleton

    Peyton Randolph

    John Hancock

      

    Continental Congress
    U.S. Presidents

    John Hancock

    Henry Laurens

    John Jay

    Samuel Huntington

      

    Constitution of 1777
    U.S. Presidents

    Samuel Huntington

    Samuel Johnston
    Elected but declined the office

    Thomas McKean

    John Hanson

    Elias Boudinot

    Thomas Mifflin

    Richard Henry Lee

    John Hancock
    [
    Chairman David Ramsay]

    Nathaniel Gorham

    Arthur St. Clair

    Cyrus Griffin

      

    Constitution of 1787
    U.S. Presidents

    George Washington 

    John Adams
    Federalist Party


    Thomas Jefferson
    Republican* Party

    James Madison 
    Republican* Party

    James Monroe
    Republican* Party

    John Quincy Adams
    Republican* Party
    Whig Party

    Andrew Jackson
    Republican* Party
    Democratic Party


    Martin Van Buren
    Democratic Party

    William H. Harrison
    Whig Party

    John Tyler
    Whig Party

    James K. Polk
    Democratic Party

    David Atchison**
    Democratic Party

    Zachary Taylor
    Whig Party

    Millard Fillmore
    Whig Party

    Franklin Pierce
    Democratic Party

    James Buchanan
    Democratic Party


    Abraham Lincoln 
    Republican Party

    Jefferson Davis***
    Democratic Party

    Andrew Johnson
    Republican Party

    Ulysses S. Grant 
    Republican Party

    Rutherford B. Hayes
    Republican Party

    James A. Garfield
    Republican Party

    Chester Arthur 
    Republican Party

    Grover Cleveland
    Democratic Party

    Benjamin Harrison
    Republican Party

    Grover Cleveland 
    Democratic Party

    William McKinley
    Republican Party

    Theodore Roosevelt
    Republican Party

    William H. Taft 
    Republican Party

    Woodrow Wilson
    Democratic Party

    Warren G. Harding 
    Republican Party

    Calvin Coolidge
    Republican Party

    Herbert C. Hoover
    Republican Party

    Franklin D. Roosevelt
    Democratic Party

    Harry S. Truman
    Democratic Party

    Dwight D. Eisenhower
    Republican Party

    John F. Kennedy
    Democratic Party

    Lyndon B. Johnson 
    Democratic Party 

    Richard M. Nixon 
    Republican Party

    Gerald R. Ford 
    Republican Party

    James Earl Carter, Jr. 
    Democratic Party

    Ronald Wilson Reagan 
    Republican Party

    George H. W. Bush
    Republican Party 

    William Jefferson Clinton
    Democratic Party

    George W. Bush 
    Republican Party

    Barack H. Obama
    Democratic Party

    Please Visit

    Forgotten Founders
    Norwich, CT

    Annapolis Continental
    Congress Society


    U.S. Presidency
    & Hospitality

    © Stan Klos

     

     

     

     


    Virtual Museum of Art | Virtual Museum of History | Virtual Public Library | Virtual Science Center | Virtual Museum of Natural History | Virtual War Museum