// Bad Behavior Start $txt['permissionname_badbehavior_goodgroup'] = 'Bad Behavior Whitelist Group'; $txt['permissionhelp_badbehavior_goodgroup'] = 'This option will make a member group exempt from all Bad Behavior tests.'; // Bad Behavior End // Begin Auto Embed Media Pro Text Strings $txt['mediapro_admin'] = 'Simple Audio Video Embedder'; $txt['mediapro_settings'] = 'Settings'; $txt['mediapro_save_settings'] = 'Save Settings'; $txt['mediapro_err_cache'] = 'Cache folder not writable must fix for performance!'; // END Auto Embed Media Pro Text Strings $txt['botscout_mail_subject'] = 'Bot Attempt Stopped'; $txt['botscout_mail_body'] = 'A bot tried to register, but was stopped from doing so.' . "\n\n" . 'Bot Name: %s' . "\n" . 'Bot Email: %s' . "\n" . 'IP Address: %s'; Recounting the Rationals

Author Topic: Recounting the Rationals  (Read 48 times)

Unbeliever

  • The Archivist
  • Administrator
  • Hero Member
  • *****
  • Posts: 1574
  • Never a God around when you need one!
    • Atheist Forums
Recounting the Rationals
« on: June 30, 2018, 03:29:58 PM »
Quote
It 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
« Last Edit: June 30, 2018, 03:34:09 PM by Unbeliever »
"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