Mathematician:Georg Ferdinand Ludwig Philipp Cantor

Mathematician

Russian-born German mathematician widely regarded as the creator of set theory.

He established the importance of correspondence between sets and helped to define the concepts of infinity and well-ordered sets.

He is also famous for stating and proving Cantor's Theorem.

Nationality

German

History

• Born: 3 March 1845, St Petersburg, Russia
• Died: 6 Jan 1918, Halle, Germany

Theorems and Definitions

• Cantor's Leaky Tent
• Cantor's Tepee
• Cantor Set
• Cantor Space
• Cantor Normal Form

• Cantor-Bendixson Derivative (with Ivar Otto Bendixson)
• Cantor-Bendixson Theorem (with Ivar Otto Bendixson)
• Smith-Volterra-Cantor Set (with Henry John Stephen Smith and Vito Volterra)

• Cantor's Diagonal Argument
• Cantor's Theorem
• Heine-Cantor Theorem (with Heinrich Eduard Heine
• Cantor-Bernstein-Schröder Theorem (with Felix Bernstein and Friedrich Wilhelm Karl Ernst Schröder) (also known as Bernstein-Schröder Theorem)

• Cantor-Dedekind Hypothesis (with Julius Wilhelm Richard Dedekind)

• Real Numbers are Uncountable

Results named for Georg Ferdinand Ludwig Philipp Cantor can be found here.

Definitions of concepts named for Georg Ferdinand Ludwig Philipp Cantor can be found here.

Publications

• 1867: De aequationibus secundi gradus indeterminatis
• 1874: Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen (On a Characteristic Property of All Real Algebraic Numbers)
• 1883: Grundlagen einer allgemeinen Mannigfaltigkeitslehre (Foundations of a General Theory of Aggregates)
• 1895: Beiträge zur Begründung der transfiniten Mengenlehre (Math. Ann. Vol. 46: pp. 481 – 512)
• 1897: Beiträge zur Begründung der transfiniten Mengenlehre (Math. Ann. Vol. 49: pp. 207 – 246)
• 1915: Contributions to the Founding of the Theory of Transfinite Numbers (translated by Philip E.B. Jourdain from Beiträge zur Begründung der transfiniten Mengenlehre)

Sources

• John J. O'Connor and Edmund F. Robertson: "Georg Ferdinand Ludwig Philipp Cantor": MacTutor History of Mathematics archive

• 1937: Eric Temple Bell: Men of Mathematics: Chapter $\text{XXIX}$
• 1964: Steven A. Gaal: Point Set Topology ... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.3$: Mappings
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Cantor, Georg Ferdinand Ludwig Philipp (1845-1918)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$): Footnote $5$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cantor, Georg (1845-1918)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cantor, Georg (1845-1918)
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 2$ Countable or uncountable?
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Cantor, Georg (Ferdinand Ludwig Philipp) (1845-1918)