March 3rd, 2018, 01:31 PM  #11 
Senior Member Joined: Aug 2012 Posts: 2,045 Thanks: 584  
March 3rd, 2018, 01:33 PM  #12 
Global Moderator Joined: Dec 2006 Posts: 19,714 Thanks: 1806 
Your original post in this thread, zylo, refers to a limit that isn't defined properly. If you manage to define it, why is it a list?
Last edited by skipjack; March 3rd, 2018 at 01:35 PM. 
March 3rd, 2018, 01:57 PM  #13  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra  Quote:
Since each has the same infinite number of 1s, they seem to be equal. And thus you claim that the natural numbers are not unique. Last edited by v8archie; March 3rd, 2018 at 01:59 PM.  
March 5th, 2018, 05:05 AM  #14  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,546 Thanks: 110  Quote:
1111 is not the same as 0111. Again and again and again you are confusing representation with interpretation. Interpretation is irrelevant to OP. You asked for one, so I tried to accomodate you. If I have defined it for all n I have defined it for the limit as n approaches infinity: an unending sequence of digits where every digit is defined. .333333333333......... for example, WHICH IS NOT 1/3. That is YOUR interpretation of limit, not the one defined in OP, Last edited by skipjack; March 9th, 2018 at 10:03 AM.  
March 5th, 2018, 07:27 AM  #15 
Global Moderator Joined: Dec 2006 Posts: 19,714 Thanks: 1806 
Why is it a list? Referring to it as a list doesn't imply that it is a list.

March 5th, 2018, 07:28 AM  #16  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra  Quote:
 
March 5th, 2018, 07:53 AM  #17  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra  Quote:
You know that you are making this all up, so you are deliberately obfuscating in an attempt to hide the fact that what you hope to show is wrong.  
March 5th, 2018, 08:59 AM  #18  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,546 Thanks: 110  Quote:
EDIT v8archie. I simply observed that you could associate a natural number with every member of the list, which puts it in numerical order, for all n. I acknowledge your opinion that for all n doesn't include infinity. Last edited by zylo; March 5th, 2018 at 09:13 AM.  
March 5th, 2018, 09:57 AM  #19 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra 
Perhaps you could try answering the questions I asked then instead of continually deflecting. You can start with: what is the second entry in the limiting case? PS: it's not an opinion that for all $n$ doesn't include "infinity", it's a fact. 
March 5th, 2018, 10:40 AM  #20 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  

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binary, cantor, infinite, sequence 
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