another proof of cardinality of the rationals

If we have a rational numberPlanetmathPlanetmathPlanetmath p/q with p and q having no common factor, and each expressed in base 10 then we can view p/q as a base 11 integer, where the digits are 0,1,2,,9 and /. That is, slash (/) is a symbol for a digit. For example, the rational 3/2 corresponds to the integer 3112+1011+2. The rational -3/2 corresponds to the integer -(3112+1011+2).

This gives a one-to-one map into the integers so the cardinality of the rationals is at most the cardinality of the integers. So the rationals are countableMathworldPlanetmath.

Title another proof of cardinality of the rationals
Canonical name AnotherProofOfCardinalityOfTheRationals
Date of creation 2013-03-22 16:01:49
Last modified on 2013-03-22 16:01:49
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 10
Author Mathprof (13753)
Entry type Proof
Classification msc 03E10