// 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 340 times)


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Recounting the Rationals
« on: June 30, 2018, 03:29:58 PM »
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.


Infinite Fractions:
« Last Edit: June 30, 2018, 03:34:09 PM by Unbeliever »
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