Problem 1471. Index of a Rational number
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. http://en.wikipedia.org/wiki/Rational_numbers
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
Problem Comments
-
2 Comments
Problem with test 4
I am not able to submit a solution. I get error "There was an issue submitting your solution. Remove inappropriate content. For guidelines, see About Cody"
Solution Comments
Show commentsProblem Recent Solvers107
Suggested Problems
-
Number of 1s in the Binary Representation of a Number
442 Solvers
-
543 Solvers
-
Flip the main diagonal of a matrix
791 Solvers
-
13063 Solvers
-
Side of an equilateral triangle
6006 Solvers
More from this Author10
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!