Thread: Ordeerd Pairs

for an Ordered Pair (m,n) I use the Encoding Method = ((m+n)(m+n+1)/2)+n for encoding this ordered pair into a single number, this helps me to find an enumeration for functions , so if I have a function that takes 2 arguments an an Input I encode them using this Mathmatical method , But my Question if I want to decode any number in an Ordered Pair , how to do this?

I appreciate your help, I am a master of science in computer science student , and I attend the course of Computability theory.


thanks for all

Caio

Originally Posted by Fahed

for an Ordered Pair (m,n) I use the Encoding Method = ((m+n)(m+n+1)/2)+n for encoding this ordered pair into a single number, this helps me to find an enumeration for functions , so if I have a function that takes 2 arguments an an Input I encode them using this Mathmatical method , But my Question if I want to decode any number in an Ordered Pair , how to do this?

My computations show that, if you are given the encoding , then, letting (integer part of (...)), you have and you deduce .

A hint about the origin of my formula: the number inside the integer part is the positive solution to the equation . And you must have (if you know where your formula comes from, this should be clear)

Thanks A lot Man I appreciate your help.
Again thanks a lot .

Regards
Fahed