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Topic: Infinitude of the prime numbers


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In the News (Wed 23 Dec 09)

  
  Number
A new number was invented, the square root of negative one, denoted by i, a symbol assigned to this new number by Leonhard Euler.
Sets of numbers that are not subsets of the complex numbers include the quaternions, invented by Sir William Rowan Hamilton, in which multiplication is not commutative, and the octonions, in which multiplication is not associative.
The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields.
www.brainyencyclopedia.com /encyclopedia/n/nu/number.html   (3674 words)

  
 Euclid - Wikipedia, the free encyclopedia
Within it, the properties of geometrical objects are deduced from a small set of axioms, thereby founding the axiomatic method of mathematics.
Although best-known for its geometric results, the Elements also includes various results in number theory, such as the connection between perfect numbers and Mersenne primes.
In particular, Euclid's proof of the infinitude of prime numbers is in Book IX, Proposition 20.
en.wikipedia.org /wiki/Euclid   (745 words)

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