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Picture of the Rational Numbers: Dense but Not Complete

Joe Frank Allison

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Abstract

The rational numbers have the propty that for any two distinct rational numbers, say a and b, with a < b, there ists another rational number c, distinct om both a and b and such that a << b. For example, c = (a + b)/2 is such a number.

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What this paper is about

The rational numbers have the propty that for any two distinct rational numbers, say a and b, with a < b, there ists another rational number c, distinct om both a and b and such that a << b. For example, c = (a + b)/2 is such a number.

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Available abstract

The rational numbers have the propty that for any two distinct rational numbers, say a and b, with a < b, there ists another rational number c, distinct om both a and b and such that a << b. For example, c = (a + b)/2 is such a number.

Key concepts: Rational number, Mathematics, Rational point, Combinatorics, Algebraic number, Mathematical analysis

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