biblografy for rational numbers in one page please
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In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.[1] Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q (or blackboard bold {\displaystyle \mathbb {Q} }\mathbb {Q} , Unicode /ℚ);[2][3] it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient".
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A one-to-one correspondence between positive binary numbers and positive rational numbers is defined and studied. Efficient algorithms to compute the rational number for a given binary ordinal number and to compute the binary ordinal number for a given rational number are presented and analyzed. This one-to-one correspondence and the related algorithms provide a link between the well-known problem of counting rational numbers and a key topic in computer science: binary numbers. The binary ordinal number of a rational and that of its reciprocal are shown to be related in a simple manner.
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