Problem 1471. Index of a Rational number

Created by G K in Community

The set of real numbers are infinite. They are so many that real numbers can't even be enumerated. However, unlike real numbers the set of integers is countably infinite as a mapping from 1,2,3,4,5 .... to 0,1,-1,2,-2,3,-3 can be made easily.

Surprisingly, rational Numbers are countably infinite too !!, meaning they can be enumerated. A diagonalization argument introduced by George Cantor easily shows this. Recollect that rational numbers are those numbers that can be represented in the form p/q.

ex: The first ten rational numbers under this enumeration are 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4.

Find the index of a positive rational number enumerated this way. ie the index of 1/3 is 6

Problem 1) Next: 1472

Solution Stats

78.35% Correct | 21.65% Incorrect
Last solution submitted on Jun 07, 2019

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