Infinity (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Infinity


00:00:38 1 History
00:01:16 1.1 Early Greek
00:01:54 1.2 Early Indian
00:02:33 1.3 17th century
00:03:11 2 Mathematics
00:03:49 2.1 Infinity symbol
00:04:28 2.2 Calculus
00:05:06 2.2.1 Real analysis
00:06:03 2.2.2 Complex analysis
00:06:42 2.3 Nonstandard analysis
00:07:20 2.4 Set theory
00:07:58 2.4.1 Cardinality of the continuum
00:08:17 2.5 Geometry and topology
00:08:56 2.6 Fractals
00:09:34 2.7 Mathematics without infinity
00:10:12 3 Physics
00:10:51 3.1 Cosmology
00:11:29 4 Logic
00:12:07 5 Computing
00:12:46 6 Arts, games, and cognitive sciences
00:13:24 7 See also
00:14:02 8 Notes
00:14:40 9 References



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SUMMARY
=======
Infinity (symbol: 
  
    
      
        ∞
      
    
    {\displaystyle \infty }
  ) is a concept describing something without any bound, or something larger than any natural number. Philosophers have speculated about the nature of the infinite, for example Zeno of Elea, who proposed many paradoxes involving infinity, and Eudoxus of Cnidus, who used the idea of infinitely small quantities in his method of exhaustion. This idea is also at the basis of infinitesimal calculus.
At the end of 19th century, Georg Cantor introduced and studied infinite sets and infinite numbers, which are now an essential part of the foundation of mathematics. For example, in modern mathematics, a line is commonly viewed as the set of all its points, and their infinite number (the cardinality of the line) is larger than the number of integers. Thus the mathematical concept of infinity refines and extends the old philosophical concept. It is used everywhere in mathematics, even in areas such as combinatorics and number theory that may seem to have nothing to do with it. For example, Wiles's proof of Fermat's Last Theorem uses the existence of very large infinite sets.
The concept of infinity is also used in physics and the other sciences.