July 9th, 2018, 10:00 AM  #71 
Senior Member Joined: Oct 2009 Posts: 498 Thanks: 164  
July 9th, 2018, 10:10 AM  #72  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,462 Thanks: 106  Quote:
Skipjack. If you don't like 1,2,3,4,.... as a primary counting mechanism, perhaps you prefer sticks and stones \ \\ \\\ \\\\ . . or 0 00 000 0000 . .  
July 9th, 2018, 10:22 AM  #73 
Global Moderator Joined: Dec 2006 Posts: 19,542 Thanks: 1752  That doesn't work because (a) 1, 2, 3, 4, ... (continued without end) doesn't contain the answer for the entire list; (b) your method doesn't satisfy the criterion "without a number system" ("counting mechanism" seems to be just an alternative phrase for "number system"); and (c) using a symbol such as "\" or "0" seems to be equivalent to "scratches on a rock". 
July 9th, 2018, 10:32 AM  #74 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,462 Thanks: 106 
a) Induction specifies all elements of a list. If I specify every element of an infinite sequence (calculus), have I specified every element of the sequence? b) 1,2,3,4,... IS the number system. You can't count something with itself. Note that the INFINITE harmonic series is specified by 1/1+1/2+1/3+...... Do you have a problem with that? Last edited by zylo; July 9th, 2018 at 10:46 AM. 
July 9th, 2018, 11:15 AM  #75  
Senior Member Joined: Oct 2009 Posts: 498 Thanks: 164  Quote:
 
July 9th, 2018, 11:26 AM  #76 
Global Moderator Joined: Dec 2006 Posts: 19,542 Thanks: 1752 
Your response, zylo, to (a) relates to the elements only. Specifying the elements isn't the same as counting the entire endless list. Your response to (b) is inapplicable, as I didn't ask you to count something with itself. I asked how you would count 1, 2, 3, 4, ... (continued without end) without a number system. As you didn't respond to (c), I assume you now accept that your suggestions that used repetitions of "\" and "0" violate the criterion that you don't use sticks, stones and the like, because you've already withdrawn that type of response. 
July 9th, 2018, 05:30 PM  #77 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,403 Thanks: 2477 Math Focus: Mainly analysis and algebra  

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anomaly, decimal, representation 
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