Georg Cantor :Life and Accomplishments

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Georg CantorLife and Accomplishments

• Erick Gonzalez
• Juan Favela
• Jacob Bautista

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Life/Leben

• Georg Ferdinand Ludwig Philipp Cantor
• March 3, 1845
• Valley
• Oldest of 6 children
• Baptized as Lutherans devoted Christian
• 3 0ut of 20 letter books
• Bacon/Shakespear
• the Realschule in Darmstadt, the Federal
  Polytechnic Institute, University of Berlin

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• Probleme des Unendlichen Werk und Leben Georg
  Cantors (1967)
• Beitrage (of 1895 1897)
• 1862 devoted his life to Math
• Leopold Kronecker, continuum hypothesis
• 1896 mother, 3 years later brother
• Artist

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1-to-1

• Correspondence between line segment and unit
  square
• for any positive integer n, there exists a
  1-to-1 correspondence between the points in an
  n-dimensional space.
• 1 -gt A
• 2 -gt B
• 3 -gt C
• 4 -gt D

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The Set Theory

• Branch of Math was in an article called ("On a
  Property of the Collection of All Real Algebraic
  Numbers").
• Proved that real numbers and positive integers
  are not equinumerous.

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Continuum Hypothesis

• Created in 1877 about the possible sizes of
  infinite sets
• There is no set whose cardinality is strictly
  between that of the integers and that of the real
  numbers.

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Cont.

• First stated the cardinality of the set of
  integers is strictly smaller than that of the set
  of real numbers
• Cantors First Uncountability Proof and Cantors
  Diagonal Argument
• Hypothesis proves the extent of the cardinality

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Death

• Nervous Breakdowns
• Heart Failure
• Died January 6, 1918

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References

• Dauben, Joseph Warren. 1979 Georg Cantor, His
  Mathematics and Philosophy of the Infinite Ch. 1
  Pg. 1-5, Ch.6 Pg. 120-148
• Everdell, William R. The First Moderns. 1997
• http//en.wikipedia.org/wiki/Georg_Cantor