July 9th, 2018, 11:00 AM  #71 
Senior Member Joined: Oct 2009 Posts: 684 Thanks: 223  
July 9th, 2018, 11:10 AM  #72  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,621 Thanks: 117  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, 11:22 AM  #73 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902  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, 11:32 AM  #74 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,621 Thanks: 117 
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 11:46 AM. 
July 9th, 2018, 12:15 PM  #75  
Senior Member Joined: Oct 2009 Posts: 684 Thanks: 223  Quote:
 
July 9th, 2018, 12:26 PM  #76 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902 
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repetitions of "\" and "0" violate the criterion that you don't use sticks, stones and the like, because you've already withdrawn that type of response.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, 06:30 PM  #77 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2552 Math Focus: Mainly analysis and algebra  

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anomaly, decimal, representation 
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