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**Georg Cantor :Life 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 -> A 2 -> B 3 -> C 4 -> 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” Cantor’s First Uncountability Proof and Cantor’s 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 “Georg Cantor, His Mathematics and Philosophy of the Infinite” Ch. 1 Pg. 1-5, Ch.6 Pg Everdell, William R. “The First Moderns”. 1997

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1-1 Copyright © 2013, 2005, 2001 Pearson Education, Inc. Section 2.4, Slide 1 Chapter 2 Sets and Functions.

1-1 Copyright © 2013, 2005, 2001 Pearson Education, Inc. Section 2.4, Slide 1 Chapter 2 Sets and Functions.

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