[Home]History of Rational numbers

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Revision 7 . . (edit) July 18, 2001 12:44 am by (logged).197.2.xxx
Revision 6 . . July 3, 2001 5:20 am by Lee Daniel Crocker
Revision 5 . . March 13, 2001 4:23 am by (logged).bmc.com
  

Difference (from prior major revision) (minor diff, author diff)

Changed: 1,11c1
The rational numbers are those which may be expressed as the ratio between two integers, where the denominator? is not equal to zero. They are commonly called `fractions'.

Mathematically we may define them as an ordered pair of integers (a,b), with b not equal to zero. We define the following operations:
:: (a,b) + (c,d) = (a*d + b*c,b*d)
:: (a,b) * (c,d) = (a*c,b*d)
To conform to our expectation that 2/4 = 1/2, we consider (a,b) to be equivalent to (c,d) if, and only if, a*d = b*c.

So defined, the set of rational numbers, Q, forms a field. It may be shown that Q is the smallest field which contains the integers.

See also:
* real numbers
#REDIRECT Rational_number

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