Difference between revisions of "Integer"

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(with the basics having been so poorly defined, there would be no reason to mix in stuff which is way over the head of most readers)
(long sentence should be a bulleted list)
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More precisely, the set of all integers consists of all natural numbers {1, 2, 3, 4, ...}, their negatives {-1, -2, -3, -4, ...} and 0.  A formal definition is that it is the only [[integral domain]] whose positive elements are well ordered and in which order is preserved by addition.
 
More precisely, the set of all integers consists of all natural numbers {1, 2, 3, 4, ...}, their negatives {-1, -2, -3, -4, ...} and 0.  A formal definition is that it is the only [[integral domain]] whose positive elements are well ordered and in which order is preserved by addition.
  
An integer may be [[even number|even]] (divisible by two) or [[odd number|odd]] (not divisible by two), [[positive number|positive]] (more than [[zero]]) or [[negative number|negative]] (less than zero), [[whole number|whole]] (undivided) or composite (divisible into other integers), and various other classifications, such as [[prime]] (only divisible by itself and one).
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An integer may be:
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* [[even number|even]] (divisible by two)
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* [[odd number|odd]] (not divisible by two)
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* [[positive number|positive]] (more than [[zero]])
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* [[negative number|negative]] (less than zero)
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* [[whole number|whole]] (undivided)
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* [[composite]] (divisible into other integers) or [[prime]] (only divisible by itself and one)
  
 
Every integer larger than 1 has a unique [[prime factorization]].
 
Every integer larger than 1 has a unique [[prime factorization]].

Revision as of 17:49, November 19, 2008

An integer is any whole number, positive, negative, or 0. Starting at 1 and going up are the counting numbers {1, 2, 3, 4, ...}, sometimes called "natural numbers".

More precisely, the set of all integers consists of all natural numbers {1, 2, 3, 4, ...}, their negatives {-1, -2, -3, -4, ...} and 0. A formal definition is that it is the only integral domain whose positive elements are well ordered and in which order is preserved by addition.

An integer may be:

Every integer larger than 1 has a unique prime factorization.

Some examples of integers: 1, 10/5, 98058493, -87, -3/3, both square roots of 9, and 0.

Likewise, the following numbers are not integers: 5/10, the square root of -9, 8.75, and pi.

See also: