Georg Cantor
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| - | The literary works of Argentine author '''[[Jorge Luis Borges]]''' contain references to several ideas in modern '''[[mathematics]]'''. These include notions such as [[set theory]], [[recursion]], [[chaos theory|chaos]], and [[infinite sequences]], although Borges' strongest links to mathematics are through [[Georg Cantor]]'s theory of infinite sets. The title of Borges' short story "[[The Aleph (short story)|The Aleph]]" is an allusion to Cantor's use of the Hebrew letter [[aleph]] (<math>\aleph</math>) to denote cardinality of [[set theory|transfinite set]]s. In particular, some of Borges' most popular works such as "[[The Library of Babel]]", "[[The Garden of Forking Paths]]", "The Aleph", "[[The Approach to Al-Mu'tasim]]" illustrate his use of mathematics. | + | |
| + | '''Georg Ferdinand Ludwig Philipp Cantor''' (1845 February 19 – January 6, 1918) was a [[Germans|German]] [[mathematician]], best known as the inventor of [[set theory]], which has become a [[foundations of mathematics|fundamental theory]] in mathematics. Cantor established the importance of [[one-to-one correspondence]] between the members of two sets, defined [[infinite set|infinite]] and [[well-order|well-ordered sets]], and proved that the [[real number]]s are "more numerous" than the [[natural number]]s. In fact, Cantor's method of proof of this theorem implies the existence of an "[[infinity]] of infinities". He defined the [[cardinal number|cardinal]] and [[ordinal number|ordinal]] numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware. | ||
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| + | ==See also== | ||
| + | * [[Cantor cube]] | ||
| + | * [[Cantor function]] | ||
| + | * [[Cantor medal]] – award by the [[Deutsche Mathematiker-Vereinigung]] in honor of Georg Cantor. | ||
| + | * [[Cantor set]] | ||
| + | * [[Cantor space]] | ||
| + | * [[Cantor's back-and-forth method]] | ||
| + | * [[Controversy over Cantor's theory]] | ||
| + | * [[Heine–Cantor theorem]] | ||
| + | * [[Infinity]] | ||
| + | * [[List of German inventors and discoverers]] | ||
| + | * [[Pairing function]] | ||
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Georg Ferdinand Ludwig Philipp Cantor (1845 February 19 – January 6, 1918) was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.
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See also
- Cantor cube
- Cantor function
- Cantor medal – award by the Deutsche Mathematiker-Vereinigung in honor of Georg Cantor.
- Cantor set
- Cantor space
- Cantor's back-and-forth method
- Controversy over Cantor's theory
- Heine–Cantor theorem
- Infinity
- List of German inventors and discoverers
- Pairing function
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