March 28, 2024, 03:03:57 am

News:

This site is now on a new server!


Recounting the Rationals

Started by Unbeliever, June 30, 2018, 03:29:58 pm

Previous topic - Next topic

Unbeliever

June 30, 2018, 03:29:58 pm Last Edit: June 30, 2018, 03:34:09 pm by Unbeliever
QuoteIt is well known (indeed, as Paul Erd½os might have said, every child knows) that the rationals are
countable. However, the standard presentations of this fact do not give an explicit enumeration;
rather they show how to construct an enumeration. In this note we will explicitly describe a
sequence b(n) with the property that every positive rational appears exactly once as b(n)/b(n+1).
Moreover, b(n) is the solution of a quite natural counting problem.


https://www.math.upenn.edu/~wilf/website/recounting.pdf


Infinite Fractions:
https://www.youtube.com/watch?v=DpwUVExX27E
"Some say God is living there [in space]. I was looking around very attentively, but I did not see anyone there. I did not detect either angels or gods....I don't believe in God. I believe in man - his strength, his possibilities, his reason."
Gherman Titov, Soviet cosmonaut, in The Seattle Daily Ti