7 Nov 2008

The Density of the Rational Numbers


by Corry Shores
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Density is a feature of continua and analog.

The set of rational numbers is dense everywhere, which is to say that between any two different rational numbers a and b (where a is less than b), there is at least one rational number c that falls between them.

Consequently, there is an infinite number of other rational numbers between any given two (p16c).

Bronshtein, Muehlig, Musiol, and Semendyayev. Handbook of Mathematics. Berlin: Springer-Verlag, 2004.




1 comment:

  1. what about the density of an irrational number?

    ReplyDelete